Question

A random survey of 100 students asked each student to select the most preferred form of recreational activity from five choices. Following are the results of the survey:Recreational Choice Baseball JoggingGender Basketball Softball Swimming Running Tennis TotalsMale 21 5 9 12 13 60Female 9 3 1 15 12 40Totals 30 8 10 27 25 1001. Test whether the choice is independent of the gender of the respondent. Approximate the p-value of the test.2. Would we reject the null hypothesis at α = 0.05?

Answer 1

No , we would not reject the null hypothesis at α = 0.05

Explanation:

Given that a random survey of 100 students asked each student to select the most preferred form of recreational activity from five choices. Following are the results of the survey.

`H_0: Independent\\H_a: Not independent.`

(Two tailed chi square test at 5% level for testing independence between gender and sports activities)

We assume H0 to be true and prepare expected values and then calculate chi square as (O-E)^2/E where O = observed value, E = expected value

Basketball Softball Swimming running Tennis

Males 21 (18.00) [0.50] 5 (4.80) [0.01] 9 (6.00) [1.50] 12 (16.20) [1.09] 13 (15.00) [0.27] 60

Females 9 (12.00) [0.75] 3 (3.20) [0.01] 1 (4.00) [2.25] 15 (10.80) [1.63] 12 (10.00) [0.40] 40

chisquare 8.4097

p value 0.077

df 4

Since p > 5% we accept null hypothesis.

No , we would not reject the null hypothesis at α = 0.05