Korea Social Survey Analyst Grade 2 study materials
Korea Social Survey Analyst Grade 2 study resources

A sample mean and a stated normal interval

Korea Social Survey Analyst Grade 2 · Put your knowledge to work in context.

All case studies

A sample mean and a stated normal interval

For a mathematical survey-analysis exercise, a simple random sample of one hundred independent observations has mean monthly expenditure of five hundred thousand won. The population standard deviation is supplied as one hundred thousand won, and the exercise directs use of a normal critical value of 1.96 for a ninety-five percent interval. Sampling is assumed sufficiently small relative to the population that finite-population correction can be ignored. A colleague divides the population standard deviation by one hundred instead of its square root. Another describes the resulting interval as containing ninety-five percent of individual expenditures. The task is to calculate the interval under the supplied assumptions and distinguish the population mean from individual observations.

1. Calculate the interval.

Read the worked answer

The standard error is 100,000 / √100 = 10,000 won. The margin is 1.96 × 10,000 = 19,600 won, giving 480,400 to 519,600 won.

2. Explain the interpretation and both mistakes.

Read the worked answer

The interval concerns the population mean under the stated procedure. Standard error divides by√n, not n. A confidence interval for a mean is not a range containing a stated share of individual expenditures.