Determine the sample size needed to cut the Margin of Error:

Below you are given ages that were obtained by taking a random sample of 9 undergraduate students.

19 22 23 19 21 22 19 23 21

a. Calculate the point estimator and determine an interval estimate at a 99% confidence level. Interpret your results.

b. Interpret the M.E. for part a.

c. Determine the sample size needed to cut the Margin of Error in half. No interpretation is needed.

d. At a 1% significance level, use the confidence interval method to determine if the average age of students is 22. Interpret your finding.
(Show and interpret the H0 and the Ha, state and use the decision rule, make a decision, interpret the decision)

e. At a 10% significance level, use the Z or T method to determine if the average age of students is 22. Interpret your finding. (This is a continuation of the previous part, no need to state the H0, the Ha. State the decision rule based on the Z or T method, make a decision at the new α = 10%, and interpret the decision)

f. At a 1% significance level, use the P-Value method to determine if the average age of students is 22. Interpret your finding. (This is a continuation of the previous part, no need to sate the H0, the Ha. State the decision rule based on P-Value, make a decision at the new α = 1%, and interpret the decision and Interpret the P-Value)