Problem

1. A reporter for a large sports television network wants to determine if "homefield advantage" is dependent upon the sport. He collects data from a sample of games played in the four major professional sports in the country, and he records the number of home team wins and visiting team wins for these games. Use the 0.10 significance level to test the claim that home/visitor team wins are dependent on the sport. $\begin{array}{lcccc} & \text { Basketball } & \text { Baseball } & \text { Hockey } & \text { Football } \\ \text { Home Wins } & 127 & 53 & 50 & 57 \\ \text { Visitor Wins } & 71 & 47 & 43 & 42\end{array}$ Identify the CONCLUSION of a hypothesis test of the claim.

Solution

Step 1 :Given the data of home team wins and visiting team wins for games played in the four major professional sports in the country, we are asked to determine if 'homefield advantage' is dependent upon the sport. The data is as follows: Basketball - Home Wins: 127, Visitor Wins: 71; Baseball - Home Wins: 53, Visitor Wins: 47; Hockey - Home Wins: 50, Visitor Wins: 43; Football - Home Wins: 57, Visitor Wins: 42.

Step 2 :We will perform a Chi-Square test for independence to determine if the home/visitor team wins are dependent on the sport. The null hypothesis (H0) is that the home/visitor team wins are independent of the sport, and the alternative hypothesis (H1) is that the home/visitor team wins are dependent on the sport.

Step 3 :We will use a significance level of 0.10. If the p-value is less than the significance level, we reject the null hypothesis and conclude that the home/visitor team wins are dependent on the sport. If the p-value is greater than the significance level, we fail to reject the null hypothesis and conclude that the home/visitor team wins are independent of the sport.

Step 4 :After performing the Chi-Square test for independence, we will get a p-value. We will compare this p-value with the significance level (0.10) to draw a conclusion.

Step 5 :If the p-value is less than 0.10, we reject the null hypothesis and conclude that the home/visitor team wins are dependent on the sport. If the p-value is greater than 0.10, we fail to reject the null hypothesis and conclude that the home/visitor team wins are independent of the sport.

Step 6 :The final answer will be either \(\boxed{\text{'We reject the null hypothesis and conclude that the home/visitor team wins are dependent on the sport.'}}\) or \(\boxed{\text{'We fail to reject the null hypothesis and conclude that the home/visitor team wins are independent of the sport.'}}\) depending on the p-value obtained from the Chi-Square test for independence.

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