8.44 Sample size, z statistics, and the Consideration of Future Consequences scale: Here are summary data from a z test regarding scores on the Consideration of Future Consequences scale (Petrocelli, 2003): The population mean (μ) is 3.20 and the population standard deviation (σ) is 0.70. Imagine that a sample of students had a mean of 3.45.

a. Calculate the test statistic for a sample of five students.

b. Calculate the test statistic for a sample of 1000 students.

c. Calculate the test statistic for a sample of 1,000,000 students.

d. Explain why the test statistic varies so much even though the population mean, population standard deviation, and sample mean do not change.

e. Why might sample size pose a problem for hypothesis testing and the conclusions we are able to draw?