Reconsider the previous exercise.
a. Suppose the sample standard deviation of the expected spending amounts was $30. Determine and interpret a 95% confidence interval for the population mean.
b. Now suppose the sample standard deviation was $50. Recalculate a 95% confidence interval for the population mean. Comment on what’s different about the confidence interval based on the larger sample standard deviation.
c. What (if anything) must be true about the distribution of the expected spending amounts in order for these confidence intervals to be valid?

Data from previous exercise

The National Retail Federation conducted a national survey of 8,526 consumers on September 1–9, 2009. Among the findings reported were that:
• 29.6% of those surveyed said that the state of the U.S. economy would affect their Halloween spending plans;
• the average amount that the respondents said they expect to spend on Halloween is $56.31.