Question

A health club manager wants to determine whether the number of days per week that college students exercise is related to gender. A random sample of 275 college students is selected and the results are classified as shown in the table. At α 0.05, is there enough evidence to conclude that the number of days a student exercises per week is related to gender? Number of days of exercise per week Gender 0-1 2-3 4-5 6-7 Tota Male 40 53 26 5 125 Female 34 5837 11 150 Total 74 121 53 17 275 Solution Here are the null and alternative hypotheses. Ho: The number of days of exercise per week is independent of gender Ha: The number of days of exercise per week depends on gender. (Claim)

Answer 1

Lets use here chi square test.

$\chi ^{2}=\sum \frac{(Oi-Ei)^{2}}{Ei}$

J10 | Chi square test statistic value is Table of Observed frequencies Number of days of exercise per week Oi Oi-Ei (Oi-Ei) 2/Ei 1.203931204 0.072727273 0.242712843 0.386096257 1.003276003 0.060606061 0.202260702 0.321746881 3.493357223 40 33.63636 6.363636364 53 Total Gender 0-1 Male Female Total 2to3 4to5 6to7 26 28.63636 2.63636364 6 7.727273 -1.72727273 34 40.36364-6.36363636 2 37 34.36364 2.636363636 11 9.272727 1727272727 26 37 63 53 150 74 17 275 Table of Expected frequencies Chi square test statistic value is Total Gender 0-1 Male Female 40.36364 Total 2to3 4to5 6to7 p value 0.321625 33.63636 55 28.63636 7.727273 66 34.36364 9.272727 63 125 150 275 74 17

Therefore p value 0.3216 > 0.05  

We fail to reject H0.

We do not have sufficient evidence to say that , number of days a student exercises per week is related to gender.