Question

1. In a group of 66 Mummers,  the average income was $62,000 with a standard deviation of $22,000. We are interested to determine if the average income of a Mummer is significantly different than $50,000.
2. 1. Write the appropriate null and alternative hypotheses for the hypothesis test that is relevant to this problem.
   2. Find the test statistic.
   3. Find the critical value for α=0.05.
   4. What is the result of the hypothesis test? Why?
   5. Find the critical value for α=0.01.
   6. What is the result of this hypothesis test? Why?
   7. Based on the results of (d) and (f), what can be said about the 95% and 99% confidence intervals? How do you know? Do not calculate the confidence intervals to justify your answer.

Answer 1

a- d) please follow the complete hypothesis test below

e-f)

g) It can be said that both the 95% and 99% confidence interval will exclude zero as the null hypothesis is rejected above for significance level 0.05 and 0.01 which corresponds to 95% confidence and 99% confidence respectively.