I85PREP
⌘ K
Intermediate Statistician (China) study materials
Intermediate Statistician (China) study resources

Intermediate Statistician (China) practice questions

One question at a time. Build your Intermediate Statistician (China) understanding.

First 50 of 190 questions. Each one lists the choices, the correct answer, and an explanation. The checker at the top of this page saves progress in this browser when it is available.

Continue in the practice tool above to load more questions, 50 at a time.

Question 1Integrated quantitative, financial and evidence reasoning

A statistical survey team needs to sample enterprises across different industry sectors where enterprise revenues vary significantly between sectors but are relatively homogeneous within each sector. Which probability sampling method is most efficient?

  1. Stratified sampling (分层抽样) Correct answer.
  2. Simple random sampling (简单随机抽样)
  3. Cluster sampling (整群抽样)
  4. Systematic sampling (等距抽样)

Explanation

Stratified sampling (分层抽样) is the most efficient probability sampling method when the population is divided into heterogeneous subgroups (strata) that internally exhibit high homogeneity. By sampling independently within each stratum, it minimizes within-stratum variance and reduces the overall sampling error compared to simple random sampling.

Question 2Integrated quantitative, financial and evidence reasoning

In a unimodal frequency distribution of enterprise annual wage data that is positively skewed (right-skewed), what is the correct relationship among the mean, median, and mode?

  1. Mode < Median < Mean (众数 < 中位数 < 均值) Correct answer.
  2. Mean < Median < Mode (均值 < 中位数 < 众数)
  3. Median < Mode < Mean (中位数 < 众数 < 均值)
  4. Mean = Median = Mode (均值 = 中位数 = 众数)

Explanation

In a right-skewed (positively skewed) unimodal distribution, extreme high values pull the arithmetic mean to the right the most, followed by the median, while the mode remains at the peak of the curve. Thus, the relationship is Mode < Median < Mean (众数 < 中位数 < 均值).

Question 3Integrated quantitative, financial and evidence reasoning

A statistician compares the dispersion of two datasets: Group A has a mean of 500万元 and standard deviation of 50万元; Group B has a mean of 20万元 and standard deviation of 4万元. Which group has greater relative dispersion?

  1. Group B, because its coefficient of variation is 20% compared to Group A's 10% Correct answer.
  2. Group A, because its standard deviation of 50万元 is much larger than Group B's 4万元
  3. Group A, because its variance is 2,500 compared to Group B's variance of 16
  4. Both groups have identical relative dispersion because both standard deviations are positive

Explanation

The coefficient of variation ($CV = \frac{s}{\bar{x}} \times 100\%$) measures relative dispersion independent of scale or measurement units. For Group A, $CV_A = \frac{50}{500} = 10\%$. For Group B, $CV_B = \frac{4}{20} = 20\%$. Since $CV_B > CV_A$, Group B exhibits greater relative variation.

Question 4Integrated quantitative, financial and evidence reasoning

If a sample dataset yields a skewness coefficient of $\alpha_3 = +1.45$ and an excess kurtosis coefficient of $\alpha_4 - 3 = +2.10$, how should the distribution be described relative to a normal distribution?

  1. Right-skewed and leptokurtic (尖峰右偏, more peaked with heavier tails) Correct answer.
  2. Left-skewed and platykurtic (平峰左偏, flatter with lighter tails)
  3. Right-skewed and platykurtic (平峰右偏, flatter with lighter tails)
  4. Symmetric and mesokurtic (标准正态峰度)

Explanation

A positive skewness coefficient ($\alpha_3 > 0$) indicates a right-skewed (positively skewed) distribution with a longer right tail. A positive excess kurtosis ($\alpha_4 - 3 > 0$) indicates a leptokurtic distribution (尖峰厚尾), which is more peaked around the center and has fatter tails than a normal distribution.

Question 5Integrated quantitative, financial and evidence reasoning

Let $Z \sim N(0, 1)$ be a standard normal random variable and $Y \sim \chi^2(k)$ be an independent Chi-square random variable with $k$ degrees of freedom. Which distribution does the statistic $T = \frac{Z}{\sqrt{Y/k}}$ follow?

  1. Student's t-distribution with $k$ degrees of freedom ($t(k)$) Correct answer.
  2. Snedecor's F-distribution with $(1, k)$ degrees of freedom ($F(1, k)$)
  3. Standard normal distribution $N(0, 1)$
  4. Chi-square distribution with $k+1$ degrees of freedom ($\chi^2(k+1)$)

Explanation

By definition, the ratio of a standard normal variable $Z$ to the square root of an independent Chi-square variable $Y$ divided by its degrees of freedom $k$, $T = \frac{Z}{\sqrt{Y/k}}$, follows Student's t-distribution with $k$ degrees of freedom ($t(k)$).

Question 6Integrated quantitative, financial and evidence reasoning

An estimator $\hat{\theta}$ of parameter $\theta$ is considered 'unbiased' (无偏性) if and only if which mathematical condition is satisfied?

  1. $E(\hat{\theta}) = \theta$ Correct answer.
  2. $Var(\hat{\theta}) \to 0$ as $n \to \infty$
  3. $\lim_{n \to \infty} P(|\hat{\theta} - \theta| < \epsilon) = 1$
  4. $Var(\hat{\theta}) \le Var(\tilde{\theta})$ for any other estimator $\tilde{\theta}$

Explanation

Unbiasedness (无偏性) means that the mathematical expectation of the estimator equals the true population parameter: $E(\hat{\theta}) = \theta$. This ensures that across repeated sampling, the estimates do not systematically deviate above or below the true value.

Question 7Integrated quantitative, financial and evidence reasoning

A random sample of $n = 64$ workers from a manufacturing plant yields a sample mean output of $\bar{x} = 120$ units. The population standard deviation is known to be $\sigma = 16$ units. What is the 95% confidence interval for the population mean $\mu$ (using $z_{0.025} = 1.96$)?

  1. [116.08, 123.92] Correct answer.
  2. [115.10, 124.90]
  3. [118.04, 121.96]
  4. [104.00, 136.00]

Explanation

When population standard deviation $\sigma$ is known, the confidence interval formula is $\bar{x} \pm z_{\alpha/2} \frac{\sigma}{\sqrt{n}}$. Standard error is $\frac{\sigma}{\sqrt{n}} = \frac{16}{\sqrt{64}} = \frac{16}{8} = 2.0$. Margin of error is $E = 1.96 \times 2.0 = 3.92$. Thus, the 95% confidence interval is $120 \pm 3.92 = [116.08, 123.92]$.

Question 8Integrated quantitative, financial and evidence reasoning

A market researcher wants to estimate average household monthly expenditure on organic food within a margin of error of $E = 50$ yuan at a 95% confidence level ($z_{0.025} = 1.96$). Prior pilot studies indicate a population standard deviation of $\sigma = 250$ yuan. What is the minimum required sample size?

  1. 97 Correct answer.
  2. 10
  3. 77
  4. 385

Explanation

The required sample size formula for estimating a population mean is $n = \left(\frac{z_{\alpha/2} \cdot \sigma}{E}\right)^2$. Substituting the parameters: $n = \left(\frac{1.96 \times 250}{50}\right)^2 = (1.96 \times 5)^2 = 9.8^2 = 96.04$. Rounding up to the next whole integer gives $n = 97$.

Question 9Integrated quantitative, financial and evidence reasoning

In a quality inspection sample of $n = 400$ electronic components, 60 are found to be defective ($p = 0.15$). What is the standard error of the sample proportion $\sigma_p$?

  1. 0.0179 Correct answer.
  2. 0.0357
  3. 0.0003
  4. 0.1275

Explanation

The standard error of the sample proportion is calculated as $SE(p) = \sqrt{\frac{p(1-p)}{n}}$. With $p = 0.15$ and $n = 400$: $SE(p) = \sqrt{\frac{0.15 \times 0.85}{400}} = \sqrt{\frac{0.1275}{400}} = \sqrt{0.00031875} \approx 0.017853 \approx 0.0179$ (or 1.79%).

Question 10Integrated quantitative, financial and evidence reasoning

In statistical hypothesis testing, what is a Type I error (第一类错误 / 弃真错误)?

  1. Rejecting the null hypothesis $H_0$ when it is actually true Correct answer.
  2. Failing to reject the null hypothesis $H_0$ when it is actually false
  3. Rejecting the alternative hypothesis $H_1$ when it is true
  4. Setting the significance level $\alpha$ higher than the test power $1-\beta$

Explanation

A Type I error (弃真错误) occurs when the test rejects the null hypothesis $H_0$ given that $H_0$ is true. The maximum probability of committing a Type I error is denoted by $\alpha$ (the significance level of the test).

Question 11Integrated quantitative, financial and evidence reasoning

A quality control manager tests whether the mean diameter of ball bearings differs from the nominal specification $\mu_0 = 10.0\text{ mm}$. A sample of $n = 100$ bearings has mean $\bar{x} = 10.05\text{ mm}$ and known population $\sigma = 0.20\text{ mm}$. What is the calculated value of the test statistic $Z$?

  1. +2.50 Correct answer.
  2. +0.25
  3. +1.25
  4. +5.00

Explanation

The one-sample z-test statistic is $Z = \frac{\bar{x} - \mu_0}{\sigma / \sqrt{n}}$. Here $\bar{x} - \mu_0 = 10.05 - 10.0 = 0.05$, and the standard error is $\frac{\sigma}{\sqrt{n}} = \frac{0.20}{\sqrt{100}} = \frac{0.20}{10} = 0.02$. Thus $Z = \frac{0.05}{0.02} = +2.50$.

Question 12Integrated quantitative, financial and evidence reasoning

In a one-way ANOVA comparing $k = 4$ production lines with $n = 5$ observations per line (total $N = 20$), the between-group sum of squares is $SSB = 180$ and the within-group sum of squares is $SSW = 320$. What is the computed $F$-statistic?

  1. 3.00 Correct answer.
  2. 0.56
  3. 2.25
  4. 4.50

Explanation

In one-way ANOVA: between-group degrees of freedom $df_B = k - 1 = 4 - 1 = 3$; within-group degrees of freedom $df_W = N - k = 20 - 4 = 16$. Mean squares are $MSB = \frac{SSB}{df_B} = \frac{180}{3} = 60$, and $MSW = \frac{SSW}{df_W} = \frac{320}{16} = 20$. The F-statistic is $F = \frac{MSB}{MSW} = \frac{60}{20} = 3.00$.

Question 13Integrated quantitative, financial and evidence reasoning

Which of the following statements regarding the Pearson linear correlation coefficient $r$ is correct?

  1. A correlation of $r = 0$ indicates the absence of a linear relationship, but a nonlinear relationship may still exist Correct answer.
  2. A correlation of $r = -0.85$ indicates a weaker relationship than $r = +0.65$
  3. $r = 0.90$ proves that variable $X$ directly causes variable $Y$
  4. Multiplying all values of $X$ by a constant $c = 100$ will increase $r$ by a factor of 100

Explanation

The Pearson correlation coefficient $r$ measures strictly linear association. An $r = 0$ means there is no linear relationship, but the two variables may have a strong nonlinear (e.g., quadratic or circular) relationship. Correlation does not imply causation, and $r$ is scale-invariant.

Question 14Integrated quantitative, financial and evidence reasoning

In a bivariate dataset with $n = 10$ pairs of $(x, y)$, calculations show $\sum (x_i - \bar{x})^2 = 80$, $\sum (y_i - \bar{y})^2 = 500$, and $\sum (x_i - \bar{x})(y_i - \bar{y}) = 240$. What is the Ordinary Least Squares (OLS) estimate of the slope $\hat{\beta}_1$?

  1. 3.00 Correct answer.
  2. 0.48
  3. 0.33
  4. 2.08

Explanation

The OLS slope estimator in simple linear regression is $\hat{\beta}_1 = \frac{\sum (x_i - \bar{x})(y_i - \bar{y})}{\sum (x_i - \bar{x})^2} = \frac{L_{xy}}{L_{xx}}$. Substituting the given values: $\hat{\beta}_1 = \frac{240}{80} = 3.00$.

Question 15Integrated quantitative, financial and evidence reasoning

In a regression model, the Total Sum of Squares is $SST = 1,000$ and the Residual/Error Sum of Squares is $SSE = 250$. What is the coefficient of determination $R^2$, and how is it interpreted?

  1. $R^2 = 0.75$; 75% of the total variation in the dependent variable $Y$ is explained by the regression model Correct answer.
  2. $R^2 = 0.25$; 25% of the total variation in the dependent variable $Y$ is explained by the regression model
  3. $R^2 = 0.866$; the correlation coefficient between $X$ and $Y$ is positive
  4. $R^2 = 4.00$; the regression model has four times more explanatory power than error

Explanation

The coefficient of determination is $R^2 = 1 - \frac{SSE}{SST} = \frac{SSR}{SST}$. Here $R^2 = 1 - \frac{250}{1000} = 1 - 0.25 = 0.75$. It indicates that 75% of the total variability in the dependent variable $Y$ is accounted for by the explanatory variable(s) in the regression model.

Question 16Integrated quantitative, financial and evidence reasoning

In simple linear regression ($Y = \beta_0 + \beta_1 X + \epsilon$), what is the mathematical relationship between the $F$-test statistic for the overall regression equation and the $t$-test statistic for testing the slope parameter $H_0: \beta_1 = 0$?

  1. $F = t^2$ Correct answer.
  2. $F = \sqrt{t}$
  3. $F = t / 2$
  4. $F = t + df$

Explanation

In simple linear regression (one explanatory variable), the overall regression ANOVA $F$-statistic with degrees of freedom $(1, n-2)$ is mathematically identical to the square of the $t$-statistic for testing the slope coefficient: $F = t^2$. Both tests yield identical p-values.

Question 17Integrated quantitative, financial and evidence reasoning

A simple linear regression fitted on $n = 22$ observations produces a sum of squared residuals of $SSE = 180$. What is the standard error of the estimate $s_e$?

  1. 3.00 Correct answer.
  2. 2.86
  3. 9.00
  4. 0.09

Explanation

The standard error of the estimate (估计标准误差) for simple linear regression measures the dispersion of observed data points around the regression line: $s_e = \sqrt{\frac{SSE}{n - 2}}$. Substituting the values: $s_e = \sqrt{\frac{180}{22 - 2}} = \sqrt{\frac{180}{20}} = \sqrt{9} = 3.00$.

Question 18Integrated quantitative, financial and evidence reasoning

In classical time series analysis, which component represents regular, recurring fluctuations within a one-year cycle driven by natural calendar or weather patterns?

  1. Seasonal variation (季节变动 $S$) Correct answer.
  2. Secular trend (长期趋势 $T$)
  3. Cyclical variation (循环波动 $C$)
  4. Irregular variation (不规则变动 $I$)

Explanation

Seasonal variation (季节变动 $S$) refers to regular, periodic patterns that repeat within a fixed time horizon of one year or less, typically caused by climate, weather, agricultural cycles, holidays, or school schedules.

Question 19Integrated quantitative, financial and evidence reasoning

A logistics company uses simple exponential smoothing with smoothing constant $\alpha = 0.3$. If the forecast for period $t$ was $F_t = 500$ tons and the actual observed demand was $Y_t = 560$ tons, what is the forecast for period $t+1$ ($F_{t+1}$)?

  1. 518 tons Correct answer.
  2. 542 tons
  3. 530 tons
  4. 560 tons

Explanation

The simple exponential smoothing formula is $F_{t+1} = \alpha Y_t + (1 - \alpha) F_t = F_t + \alpha (Y_t - F_t)$. Substituting the parameters: $F_{t+1} = 0.3(560) + (1 - 0.3)(500) = 168 + 350 = 518$ tons (or $500 + 0.3(560 - 500) = 500 + 18 = 518$).

Question 20Integrated quantitative, financial and evidence reasoning

In a quarterly retail sales time series using a multiplicative model, the seasonal indices for Q1, Q2, and Q3 are 85%, 110%, and 95% respectively. What must be the seasonal index for Q4?

  1. 110% Correct answer.
  2. 100%
  3. 115%
  4. 90%

Explanation

In a quarterly multiplicative time series model, the four quarterly seasonal indices must sum to 400% (with an average of 100%). Therefore: $Index_{Q4} = 400\% - (85\% + 110\% + 95\%) = 400\% - 290\% = 110\%$.

Question 21Integrated quantitative, financial and evidence reasoning

An enterprise's gross industrial output grew from 100 million yuan in 2020 to 144 million yuan in 2022. Using the geometric mean method (水平法 / 几何平均法), what was the average annual growth rate over the 2-year period?

  1. 20.0% Correct answer.
  2. 22.0%
  3. 44.0%
  4. 18.5%

Explanation

Under the geometric mean method (水平法), the average annual development speed is $\bar{x} = \sqrt[n]{\frac{a_n}{a_0}} = \sqrt[2]{\frac{144}{100}} = \sqrt{1.44} = 1.20$ (or 120%). The average annual growth rate is $\bar{x} - 1 = 1.20 - 1 = 0.20 = 20.0\%$.

Question 22Integrated quantitative, financial and evidence reasoning

A basket of two commodities has the following prices and quantities: Commodity A: $p_0 = 10, q_0 = 100; p_1 = 12, q_1 = 120$. Commodity B: $p_0 = 20, q_0 = 50; p_1 = 25, q_1 = 60$. What is the Laspeyres Quantity Index $K_q^L$?

  1. 120.0% Correct answer.
  2. 125.0%
  3. 116.7%
  4. 148.0%

Explanation

The Laspeyres Quantity Index uses base period prices as weights: $K_q^L = \frac{\sum q_1 p_0}{\sum q_0 p_0}$. Base period expenditure: $\sum q_0 p_0 = (100 \times 10) + (50 \times 20) = 1,000 + 1,000 = 2,000$. Weighted reporting quantity: $\sum q_1 p_0 = (120 \times 10) + (60 \times 20) = 1,200 + 1,200 = 2,400$. Thus $K_q^L = \frac{2,400}{2,000} = 1.20 = 120.0\%$.

Question 23Integrated quantitative, financial and evidence reasoning

Which equation represents the foundational static accounting equation that serves as the mathematical basis for double-entry bookkeeping and the balance sheet?

  1. Assets = Liabilities + Owner's Equity (资产 = 负债 + 所有者权益) Correct answer.
  2. Profit = Revenue - Expenses (利润 = 收入 - 费用)
  3. Assets + Expenses = Liabilities + Owner's Equity + Revenue
  4. Net Operating Cash Flow = Net Profit + Non-Cash Expenses

Explanation

The static fundamental accounting equation is Assets = Liabilities + Owner's Equity (资产 = 负债 + 所有者权益). It establishes that all economic resources possessed by an enterprise (assets) are claimed either by creditors (liabilities) or by owners/shareholders (equity).

Question 24Integrated quantitative, financial and evidence reasoning

What is the primary difference between a primary source document (原始凭证) and an accounting entry voucher (记账凭证) in the enterprise accounting cycle?

  1. A primary source document proves that an economic transaction occurred, while a 记账凭证 is prepared by accountants assigning debit/credit accounts Correct answer.
  2. A primary source document is prepared at year-end, while a 记账凭证 is prepared daily
  3. A 记账凭证 is signed by external clients, while primary documents are strictly internal
  4. Primary source documents contain accounting debits and credits, while entry vouchers do not

Explanation

A primary source document (原始凭证, e.g., VAT invoices, warehouse receipts, bank receipts) is generated or obtained when an economic event occurs to prove its occurrence. An accounting entry voucher (记账凭证) is drafted by accounting personnel based on verified primary documents, specifying the formal debit/credit accounting entries.

Question 25Integrated quantitative, financial and evidence reasoning

In China's corporate Balance Sheet (资产负债表), how are asset items conventionally arranged and presented?

  1. In descending order of liquidity (from highest liquidity to lowest liquidity) Correct answer.
  2. In alphabetical order of asset names
  3. In ascending order of historical acquisition cost
  4. In descending order of depreciation rate

Explanation

Under PRC GAAP, asset items on the Balance Sheet are listed in descending order of liquidity (流动性由强到弱): starting with Current Assets (Cash and cash equivalents, Notes receivable, Accounts receivable, Inventories) and followed by Non-Current Assets (Fixed assets, Construction in progress, Intangible assets).

Question 26Integrated quantitative, financial and evidence reasoning

In China's multi-step Income Statement (多步式利润表), which formula correctly derives Total Profit (利润总额)?

  1. Total Profit = Operating Profit + Non-Operating Income - Non-Operating Expenses Correct answer.
  2. Total Profit = Operating Revenue - Operating Costs - Income Tax Expense
  3. Total Profit = Operating Profit - Income Tax Expense
  4. Total Profit = Gross Profit + Investment Income - Selling Expenses

Explanation

The multi-step Income Statement follows the hierarchy: (1) Operating Profit (营业利润) = Operating Revenue - Operating Costs - Taxes & Surcharges - Selling/Admin/R&D/Finance Expenses + Other Gains; (2) Total Profit (利润总额) = Operating Profit + Non-Operating Income - Non-Operating Expenses; (3) Net Profit (净利润) = Total Profit - Income Tax Expense.

Question 27Integrated quantitative, financial and evidence reasoning

Which of the following cash transactions is classified as a Cash Flow from Financing Activities (筹资活动产生的现金流量) on the Cash Flow Statement?

  1. Cash paid to distribute cash dividends to shareholders Correct answer.
  2. Cash paid to purchase machinery and production equipment
  3. Cash received from customers for goods sold
  4. Cash paid to employees as wages and salaries

Explanation

Financing activities (筹资活动) relate to changes in the size and composition of the enterprise's contributed equity capital and borrowings. Cash paid for dividend distributions, cash received from issuing stock or bonds, and cash paid to repay bank loan principal are financing cash flows.

Question 28Integrated quantitative, financial and evidence reasoning

An enterprise's balance sheet reports: Current Assets = 600万元 (including Inventories = 180万元 and Prepaid Expenses = 20万元), and Current Liabilities = 250万元. What is the enterprise's Quick Ratio (速动比率)?

  1. 1.60 Correct answer.
  2. 2.40
  3. 1.68
  4. 0.80

Explanation

The Quick Ratio (速动比率) measures immediate liquidity: $QR = \frac{\text{Quick Assets}}{\text{Current Liabilities}} = \frac{\text{Current Assets} - \text{Inventories} - \text{Prepaid Expenses}}{\text{Current Liabilities}}$. Here, $\text{Quick Assets} = 600 - 180 - 20 = 400\text{万元}$. Thus, $QR = \frac{400}{250} = 1.60$.

Question 29Integrated quantitative, financial and evidence reasoning

An enterprise has Total Assets of 1,200万元 and Total Liabilities of 480万元. During the year, it generated Earnings Before Interest and Taxes (EBIT) of 150万元 and incurred Interest Expense of 30万元. What are its Asset-Liability Ratio (资产负债率) and Interest Coverage Ratio (利息保障倍数)?

  1. Asset-Liability Ratio = 40.0%, Interest Coverage Ratio = 5.0 times Correct answer.
  2. Asset-Liability Ratio = 60.0%, Interest Coverage Ratio = 4.0 times
  3. Asset-Liability Ratio = 40.0%, Interest Coverage Ratio = 4.0 times
  4. Asset-Liability Ratio = 25.0%, Interest Coverage Ratio = 5.0 times

Explanation

The Asset-Liability Ratio (资产负债率) is $\frac{\text{Total Liabilities}}{\text{Total Assets}} \times 100\% = \frac{480}{1,200} \times 100\% = 40.0\%$. The Interest Coverage Ratio (利息保障倍数) is $\frac{\text{EBIT}}{\text{Interest Expense}} = \frac{150}{30} = 5.0\text{ times}$.

Question 30Integrated quantitative, financial and evidence reasoning

A commercial company reports annual Cost of Goods Sold (COGS) of 720万元. Its inventory was 160万元 at the beginning of the year and 200万元 at the end of the year. What is the company's Inventory Turnover Ratio (存货周转次数)?

  1. 4.0 times per year Correct answer.
  2. 3.6 times per year
  3. 4.5 times per year
  4. 2.0 times per year

Explanation

Inventory Turnover Ratio is calculated as $\frac{\text{Cost of Goods Sold}}{\text{Average Inventory}}$. Average Inventory is $\frac{\text{Beginning Inventory} + \text{Ending Inventory}}{2} = \frac{160 + 200}{2} = 180\text{万元}$. Thus, $\text{Turnover Ratio} = \frac{720}{180} = 4.0\text{ times}$.

Question 31Integrated quantitative, financial and evidence reasoning

A firm generated 800万元 in Operating Revenue, 560万元 in Cost of Goods Sold, and 80万元 in Net Profit. Average Total Assets were 1,000万元. What are its Gross Profit Margin (销售毛利率) and Return on Total Assets (总资产报酬率 / ROA)?

  1. Gross Profit Margin = 30.0%, ROA = 8.0% Correct answer.
  2. Gross Profit Margin = 70.0%, ROA = 8.0%
  3. Gross Profit Margin = 30.0%, ROA = 10.0%
  4. Gross Profit Margin = 10.0%, ROA = 8.0%

Explanation

Gross Profit Margin is $\frac{\text{Operating Revenue} - \text{COGS}}{\text{Operating Revenue}} \times 100\% = \frac{800 - 560}{800} = \frac{240}{800} = 30.0\%$. Return on Assets (ROA) based on Net Profit is $\frac{\text{Net Profit}}{\text{Average Total Assets}} \times 100\% = \frac{80}{1,000} = 8.0\%$.

Question 32Integrated quantitative, financial and evidence reasoning

How is Gross Domestic Product (GDP / 国内生产总值) defined in macroeconomic accounting?

  1. The total market value of all final goods and services produced within a country's economic territory over a specified period Correct answer.
  2. The total market value of all final goods and services produced by permanent residents of a country, regardless of geographic location
  3. The total sales revenue of all enterprises operating within the national boundary including intermediate materials
  4. The total financial wealth and capital assets owned by national citizens at year-end

Explanation

GDP (国内生产总值) is a territory-based flow measure: the total monetary/market value of all final goods and services produced by all resident units within the economic territory of a country or region during a specific period (usually a quarter or a year), before deducting consumption of fixed capital.

Question 33Integrated quantitative, financial and evidence reasoning

If a country's Gross Domestic Product (GDP) is 120万亿元, and resident units received 3.5万亿元 in primary income from abroad while non-resident units earned 4.2万亿元 in primary income domestically, what is the country's Gross National Income (GNI / 国民总收入)?

  1. 119.3万亿元 Correct answer.
  2. 120.7万亿元
  3. 127.7万亿元
  4. 112.3万亿元

Explanation

The relationship between GNI and GDP is: $GNI = GDP + \text{Net Primary Income from Abroad} = GDP + (\text{Primary Income Received from Abroad} - \text{Primary Income Paid to Abroad})$. Here, $\text{Net Primary Income} = 3.5 - 4.2 = -0.7\text{万亿元}$. Thus, $GNI = 120 + (-0.7) = 119.3\text{万亿元}$.

Question 34Integrated quantitative, financial and evidence reasoning

In 2025, an economy's Nominal GDP is 110万亿元 and its Real GDP (at constant 2020 base-year prices) is 100万亿元. What is the GDP Deflator (GDP缩减指数), and what does it measure?

  1. 110.0; the overall price level of domestically produced final goods and services has increased by 10% relative to the base year Correct answer.
  2. 90.9; the economy contracted by 9.1% in real terms
  3. 10.0; the real economic growth rate of the country
  4. 1.10; the real interest rate differential

Explanation

The GDP Deflator is calculated as $\text{GDP Deflator} = \frac{\text{Nominal GDP}}{\text{Real GDP}} \times 100 = \frac{110}{100} \times 100 = 110.0$. It reflects the economy-wide change in prices of all domestically produced final goods and services between the base year and current year (a 10% increase).

Question 35Integrated quantitative, financial and evidence reasoning

In the Aggregate Demand-Aggregate Supply (AD-AS) model, if an external positive technology shock shifts the Short-Run Aggregate Supply (SRAS) curve to the right, what will be the resulting impact on equilibrium real output and the price level?

  1. Real output increases and the price level decreases Correct answer.
  2. Real output decreases and the price level increases
  3. Both real output and the price level increase
  4. Both real output and the price level decrease

Explanation

A rightward shift in the Short-Run Aggregate Supply (SRAS) curve increases total productive capacity, lowering marginal production costs. In the AD-AS framework, moving along a downward-sloping Aggregate Demand (AD) curve leads to a new equilibrium with higher real output ($Y \uparrow$) and a lower aggregate price level ($P \downarrow$).

Question 36Integrated quantitative, financial and evidence reasoning

Which of the following policy actions is an example of an expansionary (proactive) fiscal policy (积极的财政政策)?

  1. Increasing government infrastructure investment spending and cutting corporate taxes Correct answer.
  2. Raising the central bank reserve requirement ratio (RRR)
  3. Increasing statutory personal income tax rates
  4. Reducing government transfer payments and issuing contractionary directives

Explanation

Expansionary fiscal policy (积极/扩张性财政政策) aims to stimulate aggregate demand by increasing government expenditures (e.g., infrastructure public works, government procurement) and/or reducing taxes (tax cuts and fee reductions), which leaves more disposable income with firms and households.

Question 37Integrated quantitative, financial and evidence reasoning

How do 'automatic stabilizers' (自动稳定器) operate to moderate economic cycles without requiring active legislative interventions by the government?

  1. Progressive income tax revenues automatically rise and unemployment benefit payouts fall during economic booms, dampening overheating Correct answer.
  2. The central bank automatically lowers benchmark lending interest rates when GDP growth decelerates
  3. Commercial banks automatically increase credit quotas when inflation rises
  4. Exchange rates automatically appreciate to eliminate trade deficits

Explanation

Automatic fiscal stabilizers are built-in institutional mechanisms: (1) Under progressive income taxes, as national income surges during a boom, tax revenues rise disproportionately faster, curbing excess demand; (2) Unemployment insurance and transfer payments automatically expand during recessions as more people qualify, propping up consumption without waiting for new legislation.

Question 38Integrated quantitative, financial and evidence reasoning

What type of inflation is triggered when an abrupt surge in international crude oil and raw material prices significantly elevates domestic production costs across industries?

  1. Cost-push inflation (成本推动型通货膨胀) Correct answer.
  2. Demand-pull inflation (需求拉动型通货膨胀)
  3. Structural inflation (结构型通货膨胀)
  4. Hyperinflation (恶性通货膨胀)

Explanation

Cost-push inflation (成本推动型通货膨胀) occurs when aggregate supply decreases due to sharp increases in the costs of production inputs (such as wages, imported energy, raw materials, or indirect taxes), shifting the aggregate supply curve upward/leftward.

Question 39Integrated quantitative, financial and evidence reasoning

China adopts the direct quotation method (直接标价法) for foreign exchange. If the exchange rate moves from 100 USD = 710 RMB to 100 USD = 725 RMB, what does this change signify?

  1. The US Dollar has appreciated (升值) and the RMB has depreciated (贬值) Correct answer.
  2. The US Dollar has depreciated and the RMB has appreciated
  3. Both currencies have depreciated against gold
  4. The purchasing power of the RMB in international markets has increased

Explanation

Under the direct quotation method (直接标价法), the price of one unit (or 100 units) of foreign currency is expressed in terms of the domestic currency. An increase from 710 RMB to 725 RMB per 100 USD means more RMB is required to purchase the same amount of foreign currency, representing an appreciation of the USD and a depreciation of the RMB.

Question 40Integrated quantitative, financial and evidence reasoning

Which accounting method is adopted to calculate Gross Agricultural Output Value (农林牧渔业总产值)?

  1. Product Approach (产品法: summing the physical output of all agricultural products multiplied by their respective unit prices) Correct answer.
  2. Factory Method (工厂法: deducting intra-farm intermediate seed transfers)
  3. Cost-Plus Pricing Method based on total farm labor hours
  4. Expenditure Method based on rural household grain purchases

Explanation

Gross Agricultural Output Value is calculated using the Product Approach (产品法): $\text{Gross Output} = \sum (\text{Physical Output of Agricultural Products} \times \text{Unit Price})$. Unlike the industrial factory method, agriculture calculates output on an individual primary product basis across farming, forestry, animal husbandry, fishery, and agricultural support services.

Question 41Integrated quantitative, financial and evidence reasoning

How does the National Bureau of Statistics conduct national grain yield surveys (粮食产量抽样调查) to prevent statistical reporting distortion?

  1. Using multi-stage stratified cluster sampling combined with real-field crop cutting and weighing (实割实测) by NBS survey teams Correct answer.
  2. Relying entirely on self-reported estimates submitted by village committee leaders
  3. Estimating grain yield solely based on rainfall meteorological satellite radar data without field visits
  4. Multiplying agricultural fertilizer sales volume by a fixed grain conversion ratio

Explanation

To ensure objective and unbiased grain statistics, the NBS utilizes multi-stage stratified cluster sampling to select sample counties, sample villages, and sample plots. Official survey corps conduct direct on-site crop cutting, threshing, drying, and weighing (实割实测), calculating accurate per-mu yields independently of local administrative intervention.

Question 42Integrated quantitative, financial and evidence reasoning

What is the fundamental principle of the 'Factory Method' (工厂法) used to calculate Gross Industrial Output Value (工业总产值)?

  1. Treating the industrial enterprise as an integrated whole, allowing no double counting of intermediate production transfers inside the enterprise Correct answer.
  2. Summing the output values of every individual workshop inside the enterprise, including internal transfers
  3. Calculating the retail market value of products after deducting distributor wholesale profit margins
  4. Multiplying total enterprise machine operating hours by the average provincial hourly wage

Explanation

The Factory Method (工厂法) treats the entire industrial enterprise as a single economic unit. Gross Industrial Output Value reflects final industrial production results of the whole enterprise: products transferred between workshops inside the enterprise cannot be repeatedly counted. It comprises finished product output, industrial processing revenue, and work-in-progress inventory changes.

Question 43Integrated quantitative, financial and evidence reasoning

How is the Industrial Capacity Utilization Rate (工业产能利用率) defined and calculated in NBS quarterly surveys?

  1. The ratio of actual industrial output to potential production capacity under normal operational conditions: $\frac{\text{Actual Output}}{\text{Production Capacity}} \times 100\%$ Correct answer.
  2. The ratio of operating profit to total fixed asset investment
  3. The percentage of total factory machines connected to the national electric power grid
  4. The proportion of full-time employees working overtime shifts during the quarter

Explanation

Industrial Capacity Utilization Rate (工业产能利用率) is the ratio of actual industrial production output to potential productive capacity under normal market and technical operating conditions (standard shifts, necessary equipment maintenance, and normal raw material supply): $\text{Capacity Utilization} = \frac{\text{Actual Output}}{\text{Production Capacity}} \times 100\%$.

Question 44Integrated quantitative, financial and evidence reasoning

Which of the following items is included in the Total Output Value of the Construction Industry (建筑业总产值)?

  1. Value of architectural construction engineering work and equipment installation engineering work Correct answer.
  2. Cost of purchasing land use rights for real estate development
  3. Sales revenue of construction machinery manufactured in independent machinery factories
  4. Interest expenses paid on commercial real estate construction loans

Explanation

Total Output Value of Construction (建筑业总产值) includes: (1) Construction engineering output value (建筑工程产值); (2) Equipment installation engineering output value (安装工程产值); (3) Building decoration and finishing output value; (4) Other construction activities (overhaul of structures, non-standard equipment manufacture on site).

Question 45Integrated quantitative, financial and evidence reasoning

In service sector statistics, what is the annual operating revenue threshold for 'Services above Designated Size' (规模以上服务业) in the Information Transmission, Software, and Information Technology Services sector?

  1. Annual operating revenue of RMB 20 million or more (年营业收入2000万元及以上) Correct answer.
  2. Annual operating revenue of RMB 10 million or more
  3. Annual operating revenue of RMB 5 million or more
  4. Annual operating revenue of RMB 50 million or more

Explanation

NBS classifies Services above Designated Size into three revenue tiers: (1) RMB 20 million+: Transport/Storage, IT/Software, Real estate services (excluding development); (2) RMB 10 million+: Leasing/Business services, Scientific research, Health, Water/Environment; (3) RMB 5 million+: Resident services, Education, Culture/Sports/Entertainment.

Question 46Integrated quantitative, financial and evidence reasoning

In demographic statistics, what is the standard temporal criterion used to classify an individual as part of the 'Resident Population' (常住人口) of a specific city or region?

  1. Living in the local city or region for 6 months or longer during the reference year (居住半年及以上) Correct answer.
  2. Having a local permanent household registration (户籍) regardless of actual residence
  3. Living in the local city for at least 30 consecutive days
  4. Owning commercial real estate property in the local municipality

Explanation

The Resident Population (常住人口) includes: (1) People living locally with local household registration; (2) People living locally for 6 months or more whose household registration is elsewhere (migrant population); (3) People with local registration who have been away for less than 6 months. 6 months (半年) is the statutory statistical demarcation line.

Question 47Integrated quantitative, financial and evidence reasoning

In national energy statistics, 1 kilogram of Standard Coal Equivalent (1 kgce / 千克标准煤) has a standard low calorific heat value of how many kilocalories (kcal) and kilojoules (kJ)?

  1. 7,000 kcal (29,307.6 kJ) Correct answer.
  2. 5,000 kcal (20,934.0 kJ)
  3. 10,000 kcal (41,868.0 kJ)
  4. 1,000 kcal (4,186.8 kJ)

Explanation

In Chinese and international energy statistics standards: 1 kilogram of standard coal equivalent (1 kgce) is defined as having a net calorific value of exactly 7,000 kcal = 29,307.6 kJ (29.3076 MJ). 1 ton of standard coal equivalent (1 tce) equals 1,000 kgce = 7 million kcal = 29.3076 GJ.

Question 48Integrated quantitative, financial and evidence reasoning

In a standard symmetric Input-Output Table (投入产出表), what does Quadrant I (第I象限 / 中间使用与中间投入) represent?

  1. Intermediate transactions matrix ($Z_{ij}$), displaying inter-industry intermediate input and output flows between various economic sectors Correct answer.
  2. Final use matrix ($Y_i$), displaying final consumption, gross capital formation, and net exports
  3. Value added matrix ($V_j$), displaying compensation of employees, net taxes on production, depreciation, and operating surplus
  4. Direct income transfers between government and overseas institutional units

Explanation

In the Input-Output Table: (1) Quadrant I (第I象限) is the core intermediate matrix ($Z_{ij}$), showing inter-industry demand and supply; (2) Quadrant II (第II象限) shows Final Use (最终使用: consumption, capital formation, exports); (3) Quadrant III (第III象限) shows Gross Value Added (增加值: compensation, taxes, depreciation, surplus); (4) Quadrant IV shows non-production income distribution.

Question 49Integrated quantitative, financial and evidence reasoning

In input-output analysis, how is the direct input coefficient $a_{ij}$ defined, and which mathematical matrix expression represents the Leontief Inverse Matrix (complete consumption coefficient matrix)?

  1. $a_{ij} = \frac{z_{ij}}{X_j}$ (intermediate input of product $i$ consumed per unit of output of product $j$); Leontief Inverse is $(I - A)^{-1}$ Correct answer.
  2. $a_{ij} = \frac{X_j}{z_{ij}}$; Leontief Inverse is $(I + A)^{-1}$
  3. $a_{ij} = z_{ij} \times X_j$; Leontief Inverse is $(A - I)^2$
  4. $a_{ij} = \frac{z_{ij}}{\sum z_{ij}}$; Leontief Inverse is $A^{-1}$

Explanation

The direct input coefficient (直接消耗系数) is $a_{ij} = \frac{z_{ij}}{X_j}$, indicating the value of product $i$ directly consumed to produce one unit of total output of product $j$. The matrix equation is $X = AX + Y \implies (I - A)X = Y \implies X = (I - A)^{-1}Y$, where $(I - A)^{-1}$ is the Leontief Inverse Matrix (完全需求系数矩阵 / 列昂惕夫逆矩阵).

Question 50Integrated quantitative, financial and evidence reasoning

In the Flow of Funds Accounts (资金流量表 - 实物交易), what is the balancing item that bridges Gross Disposable Income and Gross Capital Formation for an institutional sector?

  1. Net Lending / Net Borrowing (净金融投资 / 净贷出或净借入 = Gross Savings + Capital Transfers - Gross Capital Formation) Correct answer.
  2. Foreign Exchange Reserves balance
  3. Total Domestic Stock Market Capitalization
  4. Commercial Bank Excess Reserves

Explanation

In the physical transactions account of the Flow of Funds: $\text{Gross Disposable Income} - \text{Final Consumption} = \text{Gross National Savings}$. Then, $\text{Gross Savings} + \text{Net Capital Transfers} - \text{Gross Capital Formation} = \text{Net Lending (+) / Net Borrowing (-)}$ (净金融投资 / 净贷出). This represents surplus funds available for financial investment in other sectors.