Reconsider the Previous Problem About the Age of a College $p$

Short Answer

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.
b. Calculate the test statistic.
c. Determine (as accurately as possible) the $p$ -value of the test.
d. State your test decision at the $\alpha=.10$ significance level.
e. Summarize your conclusion in context, and explain the reasoning process by which you reach this conclusion.
f. Would the $p$ -value have been larger, smaller, or the same if a larger sample size had been used and all else had turned out the same? (Do not bother to explain.)
g. Would the $p$ -value have been larger, smaller, or the same if the sample standard deviation had been smaller and all else had turned out the same? (Do not bother to explain.)
h. Would the $p$ -value have been larger, smaller, or the same if the sample mean had been smaller, and all else had turned out the same? (Do not bother to explain.)