The Battery Life Experiment
A consumer electronics company claims that its new smartphone battery lasts an average of 12 hours under continuous use. A consumer advocacy group suspects the average is less than 12 hours. They test 25 randomly selected phones and find a sample mean of 11.5 hours with a sample standard deviation of 1.8 hours. The distribution of battery life is known to be approximately normal. The group plans to conduct a one-sample t-test at the 1% significance level. However, they are unsure whether to use a one-tailed or two-tailed test, and they also want to check if the sample size is sufficient for the t-test to be valid.
1. Should the group use a one-tailed or two-tailed test? Explain.
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A one-tailed test is appropriate because the alternative hypothesis is directional: the group suspects the average is less than 12 hours. The hypotheses are H0: μ = 12 versus Ha: μ < 12. Using a two-tailed test would be inappropriate because it would test for any difference, not specifically a decrease, and would reduce power to detect the suspected effect.
2. Check the conditions for the t-test. Is the sample size sufficient?
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Conditions: Random sample: met (25 randomly selected phones). Independence: The sample size (25) is less than 10% of all phones (assuming more than 250 produced), so independence is reasonable. Normality: The population distribution is approximately normal, so the sampling distribution of the mean is normal regardless of sample size. Thus, the t-test is valid even with n=25. The sample size is sufficient because the normality condition is met by the population distribution, not by the Central Limit Theorem.