Question

When games were sampled throughout a? season, it was found that the home team won 113 of 164 field hockey ?games, and the home team won 53 of 92 hockey games. The result from testing the claim of equal proportions are shown on the right. Does there appear to be a significant difference between the proportions of home? wins? What do you conclude about the home field? advantage? ?2-proportion test p 1 not equals p 2 z equals 1.81592721 p dash value equals 0.06938154 ModifyingAbove p with caret 1 equals 0.6890243902 ModifyingAbove p with caret 2 equals 0.5760869565 p overbar equals 0.6484375000 Does there appear to be a significant difference between the proportions of home? wins? (Use the level of significance alpha equals 0.05 . right parenthesis A. Since the? p-value is large?, there is not a significant difference. B. Since the? p-value is small?, there is a significant difference. C. Since the? p-value is small?, there is not a significant difference. D. Since the? p-value is large?, there is a significant difference. What do you conclude about the home field? advantage? (Use the level of significance alpha equals 0.05 . right parenthesis A. The advantage appears to be higher for field hockey. B. The advantage appears to be higher for hockey. C. The advantage appears to be about the same for field hockey and hockey. D. No conclusion can be drawn from the given information.

Answer 1

p1 = 113/ 164 = 0.6890244

p2 = 53 / 92 = 0.576087

p overbar = Total number of wins / Total games

= (113 + 53) / (164 + 92) = 0.6484375

Total sample size, n = 164 + 92 = 256

Standard error of the proportion, SE =

Test statistic = (p1 - p2) / SE

= (0.6890244 - 0.576087) / 0.02984114

= 3.78

P(Z > 3.78) = 0.00008

P-value = 2 * 0.00008 = 0.00016

As, p-value is less than the significance level of 0.05, we conclude that there is significant difference and the winning proportion is significantly high for field hockey. So, the correct options are

B. Since the? p-value is small?, there is a significant difference.

and

A. The advantage appears to be higher for field hockey.