8.53 Confidence intervals, effect sizes, and Valentine’s Day spending: According to the Nielsen Company, Americans spend $345 million on chocolate during the week of Valentine’s Day. Let’s assume that we know the average married person spends $45, with a population standard deviation of $16. In February 2009, the U.S. economy was in the throes of a recession. Comparing data for Valentine’s Day spending in 2009 with what is generally expected might give us some indication of the attitudes during the recession.

a. Compute the 95% confidence interval for a sample of 18 married people who spent an average of $38.

b. How does the 95% confidence interval change if the sample mean is based on 180 people?

c. If you were testing a hypothesis that things had changed under the financial circumstances of 2009 as compared to previous years, what conclusion would you draw in part

(a) versus part (b)?

d. Compute the effect size based on these data and describe the size of the effect.