Question

Select your answer. A random survey of 212 students asked each student to select the most preferred form of recreational activity from five choices. Here are the results of the survey: Basketball (1) Softball (2) Swimming (3) Tennis (5) Jogging (4) 22 Male 31 16 19 23 Female 21 16 13 27 24 Is there a relationship between gender and preferred sport? The p-value is O below 0.01 between 0.05 and 0.10 O between 0.025 and 0.05 between 0.01 and 0.025 O none of the answers provided here

Answer 1

Step 1:

Ho: The two variables gender and preferred sport are independent.

Ha: The two variables gender and preferred sport are not independent.

Step 2: Test statistics

Observed values

Data	Basketball	softball	swimming	jogging	tennis	Total
Male	31	16	19	22	23	111
female	21	16	13	27	24	101
Total	52	32	32	49	47	212

Expected values = row total * coloumn total / grand total

Expected value	Basketball	softball	swimming	jogging	tennis	Total
Male	27.2264	16.7547	16.75	25.66	24.61	111.00
female	24.77	15.25	15.25	23.34	22.39	101.00
Total	52.00	32.00	32.00	49.00	47.00	212.00

Squared distance = (Obs - exp)²/Exp

Data	Basketball	softball	swimming	jogging	tennis	Total
Male	0.523	0.034	0.301	0.521	0.105	1.484
female	0.575	0.037	0.331	0.572	0.116	1.631
Total	1.098	0.071	0.632	1.093	0.221	3.115

$\chi^{2}$ = 3.115

df = 4

p value = 0.53876824

None of the answers provided here

Step 3:

df = 4, assuming level of significance at 0.05

$\chi^{2}$ critical = 9.488

As $\chi^{2}$ (3.115) is less than $\chi^{2}$ critical, we fail to reject the Null hypothesis.

Hence we do not have sufficient evidence to believe that two variables gender and preferred sport are not independent.