Question

State the hypotheses and identify the claim, find the critical value(s), compute the test value, make the decision, summarize the results (make the appropriate statement of the results of the claim included rejection or non-rejection of the null hypothesis). Please show ALL of your work. Include a bell graph.

Four clubs were randomly selected, and quantity of their members in the clubs are noted. At = 0.01, can it be concluded that there is a dependent relationship between the clubs and the political party affiliation of its members?

Club 1 Club 2 Club 3 Club 4

Democrat 33 22 18 13

Republican 13 16 10 23

Answer 1

• Null hypothesis (H_o) : The variables clubs and political parties are independent.
• Alternative Hypothesis (H₁) : The variables clubs and political parties are dependent.

Test of Independence Statistic for chi-sq. Test given РЯ is 2. й &. ( fiij- eij eij анализ where tii Obseened to iti sol & ith Colunm corresponding мара ча corresponding eij • Expected to pri socor Column. --- follows x²-variale with (-1) (s- 1) reedom. freedom number ol и и040 jous num в Column. %

Now or eij is computed by eijs = Ri xej where ith row Ri total sum of 0 total Sum c of ith column total Cerand T

Critical value : Based on the information provided, degrees of 0.01, the nificance level the significance so the critical value freedom (2-1 (4+) = 3. for 11. 345 test is the

Expected Values Club 1 Club 2 Club 3 Club 4 Total Democrat 46x86 = 26.73 38x86 148 = 22.081 28x86 148 16.27 36x86 148 - 20.919 86 148 Republican 46x62 148 - 19.27 38x62 145 - 15.919 28x62 148 11.73 36x62 145 15.081 62 Total 46 38 28 36 148

Squared Distances Club 1 Club 2 Club 3 Club 4 Democrat (33–26.732 20573 = 1.471 (22-22.081) 22.081 0 (18-16.27) 16:27 -0.184 (13–20.919) 20.919 -2.998 (13-19.27) Republican = 2.04 (16-16.919) 15.919 = 0 (10-11.73) 11.75 = = 0.255 (23-15.081) 15.081 = 4.158

Now Y - 1.47 +2.04 + 0 +0+ tot 0.184 to 255 t 2.998 + 4.158 lloloz Since биш so we not null RESULT Calculated XL critical value may dreject Hypothesis level of significance. ConcusION : Hypo Hypothesis is not Evidence Therefore enough Claim Clubs and political parties are dependent. Since null dejected. have we to not that the