Question

Since an instant replay system for tennis was introduced a a major tournament, men challenged 1390 referee calls, with the result that 411 of the calls were overturned. Women challenged 753 referee calls, and 213 of the calls were overturned. Use a .05 significance level to test the claim that men and women have equal success in challenging calls.

Required:
a. Test the claim using a hypothesis test.
b. Consider the first sample to be the sample of male tennis players who challenged referee calls and the second sample to be the sample of female tennis players who challenged referee calls. What are the null and alternative hypotheses for the hypothesis test?
c. What is the conclusion based on the hypothesis test?

Answer 1

H0: μm − μw = 0

against the claim

Ha: μm − μw ≠ 0

Since the calculated value of z= 0.6177 does not lie in the critical region the null hypothesis is accepted that men and women have equal success in challenging calls.

Explanation:

1) Let the null and alternate hypothesis be

H0: μm − μw = 0

against the claim

Ha: μm − μw ≠ 0

2) The significance level is set at 0.05

3) The critical region is z > + 1.96 and z< -1.96

4) The test statistic

Z= p1-p2/ sqrt [pcqc( 1/n1+ 1/n2)]

Here p1= 411/ 1390= 0.2956 and p2= 213/753=0.2829

pc = 411+ 213/1390+753

pc=624/2143

pc= 0.2912

qc= 1-pc= 1-0.2912=0.7088

5) Calculations

Z= p1-p2/ sqrt [pcqc( 1/n1+ 1/n2)]

z= 0.2956-0.2829/√ 0.2912*0.7088( 1/1390+ 1/753)

z= 0.0127/ √0.2064 (0.00204)

z= 0.0127/0.02056

z= 0.6177

6) Conclusion

Since the calculated value of z= 0.6177 does not lie in the critical region the null hypothesis is accepted that men and women have equal success in challenging calls.