Question

_____ 24. State the null and alternative hypotheses. A study was conducted to determine if there is a relationship between fan preference of instant replay use and the sport in which it is applied. The category counts of 102 fans are provided in the two-way table below. Use a Chi-Square independence test to determine if fan preference of instant replay use and the sport in which it is applied are independent at the 5% level of significance. State the null and alternative hypotheses.

	favor	oppose	totals
football	19	5	24
baseball	18	6	24
basketball	15	26	41
soccer	5	8	13
totals	57	45	102

a) 0 : Instant Replay Preference is Independent of Sport : Instant Replay Preference is Dependent of Sport A H H

b) 0 : Instant Replay Preference is Dependent of Sport : Instant Replay Preference is Independent of Sport

Answer 1

Correct option is:

H 0 : Instant Replay Preference is Independent of Sport

Ha  Instant Replay Preference is Dependent of Sport

degree of freedom(df) =(rows-1)*(columns-1)=	3
for 3 df and 0.05 level , critical value       χ2=	7.815
Decision rule : reject Ho if value of test statistic X2>7.815

Applying chi square test of independence:

Expected	Ei=row total*column total/grand total	Favor	oppose	Total
	football	13.412	10.588	24.00
	basnball	13.412	10.588	24.00
	basketball	22.912	18.088	41.00
	Soccer	7.265	5.735	13.00
	total	57.00	45.00	102.00
chi square    χ2	=(Oi-Ei)2/Ei	Favor	oppose	Total
	football	2.328	2.949	5.2778
	basnball	1.570	1.9882	3.5579
	basketball	2.732	3.4606	6.1926
	Soccer	0.706	0.8943	1.6003
	total	7.3361	9.2924	16.629
test statistic X2 =	16.629

p value =

0.0008

since test statistic falls in rejection region we reject null hypothesis

we have sufficient evidence to conclude that Instant Replay Preference is Dependent of Sport