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.
   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

using excel>addin>phstat>one sample test

we have

t Test for Hypothesis of the Mean
Data
Null Hypothesis                u=	50000
Level of Significance	0.05
Sample Size	66
Sample Mean	62000
Sample Standard Deviation	22000
Intermediate Calculations
Standard Error of the Mean	2708.0128
Degrees of Freedom	65
t Test Statistic	4.4313
Two-Tail Test
Lower Critical Value	-1.9971
Upper Critical Value	1.9971
p-Value	0.0000
Reject the null hypothesis

for level of significance 0.01

Two-Tail Test
Lower Critical Value	-2.6536
Upper Critical Value	2.653

1 )the appropriate null and alternative hypotheses for the hypothesis test that is relevant to this problem is

Ho:u=50000

Ha:u 50000

2)  the test statistic is 4.4313

3) the critical value for α=0.05 are

Lower Critical Value	-1.9971
Upper Critical Value	1.9971

4) since the value of test stat is not lie in between lower and upper critical value so reject Ho

5)he critical value for α=0.01 is

Lower Critical Value	-2.6536
Upper Critical Value	2.653

6)since the value of test stat is not lie in between lower and upper critical value so reject Ho

7) we can say that both 95% and 99% confidecen interval do not contain value 50000 inside the intervals