Sports team owners are constantly in competition for good players. The better th

Question

Sports team owners are constantly in competition for good players. The better the winning percentage, the more likely the team will provide good business returns for the owners. Does the size of the payroll matter? Below is the regression showing the association between team salaries (in millions of dollars) and the number of wins for 20 teams for a recent season. Complete pans (a) through (c) below. Click the loon 10 view the regression analysis. Click the loon to view the sports team data. a) State the hypotheses about the slope. H_0: There is linear relationship between team salaries and the number of wins. H_A: There is linear relationship between team salaries and the number of wins. b) Perform the hypothesis test and state your conclusion in context. Identify the test statistic for this test. t = (Round to two decimal places as needed.) Identify the P-value for this test. The P-value is (Round to there decimal places as needed.) State the conclusion to this test in context. Use a significance level of 0.05 A. Reject the null hypothesis. There is sufficient evidence of linear relationship between salaries and wins. B. Do not reject the null hypothesis. There is insufficient evidence of a linear relationship between salaries and wins. C. Reject the hypothesis. There is insufficient evidence of a linear relationship between salaries and wins. D. Do not reject the null hypothesis. There is sufficient evidence of a linear relationship between salaries and wins. e) Using a statistics program and the provided data, check the assumptions and conditions. Is the Linearity Assumption met? A. No, the Linearity Assumption is not met because the scatterplot of the residuals either shows no pattern or a nonlinear pattern. B. No, the Linearity Assumption is not met because the scatterplot of the data shows a nonlinear pattern. C. Yes, the Linearity Assumptions is met because the scatterplot of the residuals shows a linear pattern. D. Yes, the Linearly Assumption is met because the scatterplot of the data either shows a linear pattern or no pattern at all. Is the Independence Assumption met? A. Yes, the Randomization Condition is met which is enough to ensure that the measurements are independent. B. No, the measurements are inherently dependent since a win for one teams implies a loss for another team. C. No, the data are not randomized and so any patterns may be a result of the sampling method. D. Yes, the Randomization Condition is not applicable in this scenario and the scatterplot of the residuals shows no pattern. Is the Equal Variance Assumption met? A. Yes, the scatterplot of the residuals shows roughly equal variance for all values of the independent variable. B. Yes, the scatterplot of the data shows roughly equal variances for all values of the independent variable. C. No, the scatterplot of the data does not show roughly equal variances for all value of the independent variable. D. No, the scatterplot of the residuals does not show roughly equal variance for all values of the independent variable. Is the Normal Population Assumption met? A. No, since the data are not unimodal, symmetric or bell-shaped. they do not appear to come from a distribution that follows the Normal Model. B. No, while a Normal probability plot of the residuals does not show any severe departure from Normality. there is an obvious outlier. C. Yes, since the data are unimodal, symmetric, and bell-shaped. they appear to come from a distribution that that follows the Normal Model. D. Yes, a Normal probability plot of the residuals does not show any severs departure from Normally and there are no obvious outliers.

Explanation / Answer

a) Ho : there is a linear relationship

Ha: - there is no linear lrelatonship

b) t = t-ratio in salary

= 4.95

p-value = 0.0001

since p-value is less than 0.05

we reject the null and conclude that there is sufficient evidence that there is linear relationship

hence option A) is correct

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