Question

Since an instant replay system for tennis was introduced at a major​ tournament, men challenged 1389 referee​ calls, with the result that 425 of the calls were overturned. Women challenged 767 referee​ calls and 230 of the calls were overturned. Use a 0.05 significance level to test the claim that men and women have equal success in challenging calls. Complete parts​ (a) through​ (d) below.

a. Test the claim using a hypothesis test.

b. Identify the test statistic

c. P-value

d. Confidence interval

Answer 1

(a)

H0: Null Hypothesis: p1 = p2 ( men and women have equal success in challenging calls ) (Claim)

HA: Altrnative Hypothesis: p1 p2 ( men and women have no equal success in challenging calls )

(b)

n1 = 1389

1 = 425/1389 = 0.306

n2 = 767

2 = 230/767 = 0.2999

= 0.05

From Table, critical values of Z = 1.96

Pooled Proportion is given by:

Test Statistic is given by:

(c)

By Technology, P - value = 0.7679

(d)

Confidence Interval:

= (- 0.0344 , 0.0466)

So,

Answer is:

(- 0.0344 , 0.0466)