Statist 1. Recently a survey was conducted involving customers of a fitness cent

Question

Statist 1. 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: 0-1 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 2-3 4-5 Over 5Total Males | 40 60 51 21 172 Females 110 90 Total 150 150110 1106303 475 Based on the collected data is there evidence of a relationship between gender of the customer and the number of visits made each weck. Test at the alpha- 0.05 kevel of significance. (20 points) a State the Null and Altermative Hypotheses of Interest: b. The critical valae of the test statistic is: c. Show the expected observations. 0-1 4-5 Over 5 Total Males 172 Females Tetalt 150150-t-110 | 65 | 475 d. The calculated value of the test statistic is

Explanation / Answer

a) null hypothesis: Ho: gender of customer and number of visits made each week are independent,

alternate hypothesis: Ha:gender of customer and number of visits made each week are dependent,

b)

here degree of freedom =(number of rows-1)*(number of columns-1) =(2-1)*(4-1)=3

for 0.05 level and 3 degree of freedom critical value =7.8147

c)

from above expected frequency:

d)

test statistic =12.185

e)

as test stat is higher then critical value ; therefore we reject null hypothesis.

there is sufficient evidence to conclude that

gender of customer and number of visits made each week are related.

Expected E=rowtotal*column total/grand total 0-1 2-3 4-5 over 5 Total males 54.32 54.32 39.83 23.54 172 demales 95.68 95.68 70.17 41.46 303 Total 150 150 110 65 475

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