Recently a survey was conducted involving customers of a fitness center in Boise

Question

Recently a survey was conducted involving customers of a fitness center in Boise,Idaho. Participants were asked to indicate how often they use the club by checking one of the following categories: 0-I times per week; 2-3 times per week; 4-5 times per week; more than 5 times. The following data show how males and females responded to this question: 0-1 23 45Over5 Total Males 40 60 51 172 Females 110 59 110 303 475 Total 150 150 65 Based on the collected data is there evidence of a relationship between gender of the customer and the sumber of visits made each week. Test at the alpha-0.05 level of significance. (25 points) a. State the Null and Alternative Hypctheses of Ieterest b. The critical value of the test statistic is c. Show the expected observations Over 5 Total 172 303 475 0-1 2-3 4-5 Males Females 65 Total 150 150110 d. The calculated value of the test statistic is: e. Conclusion:

Explanation / Answer

a)
H0: Gender of the customer and the number of visits made each week are indpendent

H1: Gender of the customer and the number of visits made each week are not indpendent

b)
For alpha = 0.05, df = 3
critical value = 7.815

c)

d)

Test statistics, chi-square = 12.185

e)

As value of chi-square is greater than critical value, we reject the null hypothesis.

This means there is relation between gender of customer and number of visits per week

Expected 0-1 2-3 4-5 Over 5 Males 54.316 54.316 39.832 23.537 172.000 Females 95.684 95.684 70.168 41.463 303.000 Total 150.000 150.000 110.000 65.000 475.000

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