Question

Jim conducted a survey to determine what types of exercise machine are preferred by gym members at a variety of different gyms. He also asked the respondents how long they had been a member of a gym. The results are given below. Test at the 0.05 significance level if the type of exercise machine preferred is independent of the length of time a person had been a member of a gym.

	Rower	Elliptical	Treadmill	Stationary bike
Less than a year	65	37	154	164
1-3 Years	47	158	74	180
More than 3 Years	86	245	28	146

(A) State the hypotheses.

(B) State the test statistic.

(C) Calculate the P-value.

(D) Make a decision.

(e) State the conclusion addressing the original claim.

Answer 1

A)the type of exercise machine preferred is independent of the length of time a person had been a member of a gym.

vs

the type of exercise machine preferred is dependent of the length of time a person had been a member of a gym.

B) We will perform Chi-square test for independence.

Here observed test statistic==255.16

C)p-value<2.2e-16

D)since p-value<0.05, we reject

E)With strong evidence based on the given sample data we can conclude that the type of exercise machine preferred is dependent of the length of time a person had been a member of a gym.

R OUTPUT: