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	97	100	101
Catholic	54	61	100
Jewish	15	25	24
Other	85	61	73

What can be concluded at the αα = 0.10 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?
H0:H0:

The distribution of sneaker brand is not the same for each religion.

Sneaker brand and religious affiliation are independent.

Sneaker brand and religious affiliation are dependent.

The distribution of sneaker brand is the same for each religion.

H1:H1:

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 dependent.

Sneaker brand and religious affiliation are independent.

The test-statistic for this data =  (Please show your answer to 2 decimal places.)

The p-value for this sample = (Please show your answer to 4 decimal places.)  

The p-value is Select an answer greater than less than (or equal to)  αα  

Based on this, we should

fail to reject the null

reject the null

accept the null

Thus, the final conclusion is...

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.

There is sufficient 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 insufficient evidence to conclude that sneaker brand and religious affiliation are dependent.

Answer 1

CHI SQUARE TEST OF INDEPENDENCE

NULL HYPOTHESIS H0: Sneaker brand and religious affiliation are independent.

ALTERNATIVE HYPOTHESIS Ha: Sneaker brand and religious affiliation are dependent.

alpha= 0.1

chi square statistic= 17.78

D.F= (4-1)*(3-1)= 6

P VALUE= 0.0068 < 0.1 level of significance therefore SIGNIFICANT

Decision: REJECT NULL HYPOTHESIS H0

COnclusion: There is sufficient evidence to conclude that sneaker brand and religious affiliation are dependent.