Question

do oddsmakers believe that teams who play at home will have home field advantage? specifically, do oddsmakers give higher point spreads when the favored team plays home games as compared to when the favored team plays away games? two samples were randomly selected from three complete national football league seasons (1989, 1990, and 1991). the first sample consisted of 50 games, where the favored team played in a home game, while the second sample consisted of 50 games, where the favored team played in an away game. the oddsmakers point spreads (which are the number of points by which the favored team is predicted to beat the weaker team) were then collected. the following hypotheses were tested: $h_0:mu_1 = mu_2$ $h_a:mu_1>mu_2$ analyses were run. the following is the (edited) output for the test: hypothesis test results: $mu_1$: favored team - home game $mu_2$: favored team - away game |difference|sample mean|std. err.|df|t - stat|p - value| |---|---|---|---|---|---| |$mu_1-mu_2$|0.11|0.67168534|94.155815|0.16376716|0.4351| which of the following is an appropriate conclusion based on the output? a. the data provide sufficient evidence to reject $h_0$; thus, we can conclude that the mean point spread for home games is higher than that of away games. b. the data do not provide sufficient evidence reject the $h_0$; thus, we can conclude that the mean point spread for home games is higher than that of away games. c. the data provide sufficient evidence reject the $h_0$; thus, we cannot conclude that the mean point spread of home games is higher than that of away games. d. the data do not provide sufficient evidence to reject $h_0$; thus, we cannot conclude that the mean point spread of home games is higher than that of away games.

Explanation:

Step1: Recall hypothesis - testing decision rule

In hypothesis - testing, if the p - value is greater than the significance level (commonly $\alpha = 0.05$), we fail to reject the null hypothesis $H_0$.

Step2: Identify the p - value

The p - value from the output is $0.4351$. Since $0.4351>0.05$, we do not have enough evidence to reject the null hypothesis $H_0:\mu_1=\mu_2$.

Answer:

D. The data do not provide sufficient evidence to reject $H_0$; thus, we cannot conclude that the mean point spread of home games is higher than that of away games.