Question

Since an instant replay system for tornis was introduced at a major tournament, mon challenged 1426 referee calls, with the result that 415 of the calls were overturned. Women challenged 768 referee cals, and 212 of the calls were overtumed. Use a 0.05 significance level to test the claim that men and women have equal success in challenging calls. Complete parts (a) through (c) below. Consider the first simple to be the sample of male tennis players who challenged referee calls and the second sample to be the sample of female fornis players who challenged referee calls. What are the nut and alternative hypotheses for the hypothesis test? OA HP, P2 HEPP OD HP P2 HP, P2 OB HP P2 H, P1P2 OE HP P2 OC. Hy P, P2 Hy: PHP2 OF HOP SP2 H:P1*P2 Identity The lost statistic Round to two decimal places as needed.) Identify the P-value Morut hypothesis. There evidence lo warrant rejection of the claim that women and men have equal Round to three decimal places as needed) What is the conclusion based on the typothesis test? The P-vais the significance level of 0.05.10 Success in changing als b. Tostre claim by constructing an appropriate confidence interval The confidence interval ( PP) Ford to decimal places as needed

Answer 1

Option - D) H₀: p1 = p2

H₁: p1 $\neq$ p2

= 415/1426 = 0.291

pi

= 212/768 = 0.276

p2

The pooled sample proportion (P) = (
pi
* n1 +
p2
* n2)/(n1 + n2) = (0.291 * 1426 + 0.276 * 768)/(1426 + 768) = 0.2857

SE = sqrt(P(1 - P)(1/n1 + 1/n2))

= sqrt(0.2857 * (1 - 0.2857) * (1/1426 + 1/768))

= 0.0202

The test statistic is

$z = \frac{\widehat p1 - \widehat p2}{SE}$

$= \frac{0.291 - 0.276}{0.0202}$

$=0.74$

P-value = 2 * P(Z > 0.74)

= 2 * (1 - P(Z < 0.74))

= 2 * (1 - 0.7704)  

= 0.4592

The P-value is greater than the significance level of $\alpha$ = 0.05, so do not reject the null hypothesis. There is not evidence to warrant rejection of the claim that women and men have equal success in challenging calls.

b) For 95% confidence interval, the critical value is z_0.025 = 1.96

The 95% confidence interval is

(
pi
-
p2
) +/- z_0.025 * SE

= (0.291 - 0.276) +/- 1.96 * 0.0202

= 0.015 +/- 0.04

= -0.025, 0.055

Because the confidence interval limits contains 0, there doesn't appear to be a significant difference between the two proportions. There is not evidence to warrant rejection of the claim that women and men have equal success in challenging calls.

c) Option - C) The confidence interval suggests that there is no significant difference between the success of men and women in challenging calls.