Toastmasters International cites a February 2001 report by Gallup Poll that 40% of Americans fear public speaking.† A student believes that less than 40% of students at her school fear public speaking. She randomly surveys 361 schoolmates and finds that 138 report they fear public speaking. Conduct a hypothesis test at the 5% level to determine if the percent at her school is less than 40%.
Note: If you are using a Student's t-distribution for the problem, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.) 1. State the null hypothesis. 2. State the alternative hypothesis 3.State the distribution to use for the test. (Round your standard deviation to four decimal places.) 4. What is the p-value 5. What is the test statistic? (Round your answer to two decimal places.)