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

Toastmasters International cites a report by Gallop 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 135 reports they fear public speaking. Conduct a hypothesis test to determine if the percent at her school is less than 40% at the 99% confidence level.

  1. State the null and alternate hypothesis and α.
  2. State the z- or t-value (whichever is appropriate) (Show work).
  3. What is the p-value
  4. Write a conclusion.
  5. Find a 98% confidence interval for the proportion of students that fear public speaking. (Show work)
  6. How large sample size should be used to be 95% sure that the sample proportion p^ is within a margin of error E = .05 of the population proportion of students who are afraid of public speaking.
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