1. Students in an introductory statistics class were asked to report the age of their mothers when they were born. Summary statistics include

Sample size: 28 students

Sample mean: 29.643 years

Sample standard deviation: 4.564 years

• a. Determine and interpret a 90% confidence interval for the mother's mean age (at student's birth) in the population of all students at this university.
• b. How would a 99% confidence interval compare to the 90% interval in terms of its midpoint and half-width
• c. Would you expect 90% of the ages in the sample to be within the 90% confidence interval? Explain why or why not.
• d. Even if the distribution of mothers' ages were somewhat skewed, would this confidence interval procedure still be valid with these data? Explain why or why not.

2. Reconsider the previous problem about the age of a college student's mother when the student was born. Now suppose you want to conduct a significance test of whether the sample data provide strong evidence that the population mean mother's age is less than 30 years.

• a. State the appropriate null and alternative hypotheses in symbols and clarify what the variable represents.
• b. Calculate the test statistics
• c. Determine (as accurately as possible) the p-value of the test.
• d. State your decision at the 0.10 significance level.
• e. Summarize your conclusion in context, and explain the reasoning process by which you reach this conclusion.