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.

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

hypothesis:-

$H_{0}:$ the relationship between the clubs and the political party affiliation of its members are independent.

the relationship between the clubs and the political party affiliation of its members are dependent [ claim ]

H1

the critical value = 11.345

[ df = (4-1)*(2-1) = 3

chi square critical value for alpha= 0.01, df = 3, right tailed test = 11.345 ]

the necessary calculation table :-

		club 1	club 2	club 3	club 4	row total
democrat	observed	33	22	18	13	86
	expected	(46*86)/148 =26.7297	22.0811	16.2703	20.9189
	$\frac{(obs-exp)^2}{exp}$	1.4709	0.0003	0.1839	2.9977
republican	observed	13	16	10	23	62
	expected	19.2703	15.9189	11.7297	15.0811
	$\frac{(obs-exp)^2}{exp}$	2.0403	0.0004	0.2551	4.1581
	column total	46	38	28	36	148

the test statistic be:-

$\chi^2=\sum \frac{(obs-exp)^2}{exp}\approx \mathbf{11.107}$

decision:-

$\chi^2=11.107 < 11.345$

we fail to reject the null hypothesis.

conclusion:-

There is not enough evidence to conclude that there is a dependent relationship between the clubs and the political party affiliation of its members.

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