Question

In: Statistics and Probability

Please clearly state the step number next to the answers given, thank you! A political researcher...

Please clearly state the step number next to the answers given, thank you!

A political researcher wishes to know if political affiliation and age are related. He has collected data on 283 persons in three age categories. Is there evidence that age and political affiliation are related?

Age	Democrat	Republican	Independent	Total
18-31	37	38	19	94
32-51	43	38	23	104
52-68	32	35	18	85
Total	112	111	60	283

Step 1 of 8: State the null and alternative hypothesis.
H0: political affiliation and age are dependent
Ha: political affiliation and age are independent

OR

H0: political affiliation and age are independent
Ha: political affiliation and age are dependent

Step 2 of 8: Find the expected value for the number of democrats that are 18-31 years old. Round your answer to one decimal place.
Step 3 of 8: Find the expected value for the number of republicans that are 32-51 years old. Round your answer to one decimal place.
Step 4 of 8: Find the value of the test statistic. Round your answer to three decimal places.
Step 5 of 8: Find the degrees of freedom associated with the test statistic for this problem.
Step 6 of 8: Find the critical value of the test at the 0.005 level of significance. Round your answer to three decimal places.
Step 7 of 8: Make the decision to reject or fail to reject the null hypothesis at the 0.005 level of significance.
Step 8 of 8: State the conclusion of the hypothesis test at the 0.005 level of significance. (There is sufficient evidence or there is not sufficient evidence)

Expert Solution

Step 1

H0: political affiliation and age are independent
Ha: political affiliation and age are dependent

Step 2 and Step 3 Combined

Step 4

Test Statistics

The Chi-Squared statistic is computed as follows:

Step 5

The number of degrees of freedom is

Step 6

Based on the information provided, the significance level is α=0.005 , the number of degrees of freedom is df = 4, so then the critical value is 14.86 and the rejection region for this test is

Step 7

Since it is observed that , it is then concluded that the null hypothesis is not rejected.

Step 8

It is concluded that the null hypothesis Ho is not rejected. Therefore, there is NOT enough evidence to claim that the two variables are dependent, at the 0.005 significance level.

The corresponding p-value for the test is

Let me know in the comments if anything is not clear. I will reply ASAP! Please do upvote if satisfied!

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