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

Answer:

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

Step-by-step 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