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Toastmasters International cites a report by Gallup Poll that 40% of Americans fear public speaking. A...

Toastmasters International cites a 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 137 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.)

-state the null hypothesis

-state the alternative hypothesis

- In words state what random variable P' represents

- State the distribution for the test: P'~

-what is the test statistics? z or t distribution

-What is the P value

- Explain what the P value means

- Sketch picture of the situation

- construct 95% construction interval for the true proportion

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