Question

A researcher is interested in investigating whether religious affiliation and the brand of sneakers that people wear are associated. The table below shows the results of a survey. Frequencies of Religions and Sneakers Nike Adidas Other Protestant 98 91 102 Catholic 52 52 99 Jewish 21 15 36 Other 63 65 77 What can be concluded at the α = 0.05 significance level? What is the correct statistical test to use? Independence Paired t-test Homogeneity Goodness-of-Fit What are the null and alternative hypotheses? H 0 : Sneaker brand and religious affiliation are dependent. The distribution of sneaker brand is not the same for each religion. The distribution of sneaker brand is the same for each religion. Sneaker brand and religious affiliation are independent. H 1 : Sneaker brand and religious affiliation are dependent. The distribution of sneaker brand is the same for each religion. The distribution of sneaker brand is not the same for each religion. Sneaker brand and religious affiliation are independent. The test-statistic for this data = (Please show your answer to three decimal places.) The p-value for this sample = (Please show your answer to four decimal places.) The p-value is α Based on this, we should reject the null accept the null fail to reject the null Thus, the final conclusion is... There is sufficient evidence to conclude that sneaker brand and religious affiliation are dependent. There is insufficient evidence to conclude that sneaker brand and religious affiliation are dependent. There is sufficient evidence to conclude that sneaker brand and religious affiliation are independent. There is sufficient evidence to conclude that the distribution of sneaker brand is not the same for each religion. There is insufficient evidence to conclude that the distribution of sneaker brand is not the same for each religion.

Answer 1

What is the correct statistical test to use? : Independence

Ho: Sneaker brand and religious affiliation are independent.

H1: Sneaker brand and religious affiliation are dependent.

Applying chi square test:

Expected	Ei=row total*column total/grand total	Nike	Adidas	Other	Total
	Protestant	88.32	84.17	118.51	291
	Catholic	61.61	58.71	82.67	203
	Jewish	21.85	20.82	29.32	72
	Other	62.22	59.29	83.49	205
	total	234	223	314	771
chi square    χ2	=(Oi-Ei)2/Ei	Nike	Adidas	Other	Total
	Protestant	1.0612	0.5547	2.3010	3.917
	Catholic	1.4992	0.7679	3.2238	5.491
	Jewish	0.0332	1.6293	1.5204	3.183
	Other	0.0098	0.5493	0.5043	1.063
	total	2.603	3.501	7.550	13.6541

The test-statistic for this data =13.654

  p-value for this sample = 0.0337

we should reject the null

here is sufficient evidence to conclude that sneaker brand and religious affiliation are dependent