Question

Data showing the values of several pitching statistics for a random sample of 20 pitchers from the American League of Major League Baseball is provided. Player HR/IP R/IP 0.10 0.29 0.11 0.34 0.07 0.40 Beckett, Wilson, C Sabathia, 0.07 0.37 Team DET Bos | TEX NYY LAA OAK LAA BOS SEA SEA W ERA SO/IP 245 2.00 1.00 0.91 16 0.92 0.97 0.81 0.72 11 12 0.78 15 3.47 0.95 -4 -4 2.47 0.95 Haren, D 16 10 McCarthy, B 9/ Santana, E 0.08 0.38 0.06 0.43 0.11 0.10 0.40 0.08 0.42 .42 0.42 Lester, Lester, 3 Hernandez, F Buehrle, M Colon, B hlin, Danks, NYY CLE 12 MIN . cws BAL TEX 14 DET15 T B 11 Guthrie, 10 4.00 - 2.25 132.30 124.33 134.33 10 4.40 4.43 10 4.45 4.75 0.52 0.54 0.46 0.79 0.63 0.84 0.89 0.57 0.57 0.13 0.15 0.10 0.11 0.13 0.17 0.15 0.13 0.10 0.52 0.43 0.55 0.52 0.54 0.51 0.52 0.52 0.57 Lewis, C Scherzer, M Davis, W Porcello, R DET An estimated regression equation was developed to predict the average number of runs given up per inning pitched (R/IP) given the average number of strikeouts per inning pitched (SO/IP) and the average number of home runs per inning pitched (HR/IP). B/IP - 0.5265 -0.2483 90/17 - 1.032 ER/IP (a) Use the F test to determine the overall significance of the relationship. State the null and alternative hypotheses. OH: One or more of the parameters is not equal to zero. M: F1 = 1, = 0 Ho: Ho = 0 H: All the parameters are not equal to zero. H:0 H. PO = 0 OH: f= = 0 H: One or more of the parameters is not equal to zero. Calculate the test statistic. (Round your answer to two decimal places.) Calculate the p-value. (Round your answer to three decimal places.) P-value =

Answer 1

Answer:

To test the hypothesis is that there is a significant overall relationship at 5% level of significance. The null and alternative hypothesis is, H: B = B, 0 H.B.B. 70

The F-test statistics is, 2) By using Excel software, find F-test statistics with help of following steps: 1) Import the data. Select Data Analysis from Data menu. 3) Select Regression and click Ok. Input Y Range and Input X range. 5) Click Ok. 4) SUMMARY OUTPUT ANOVA df Regression Residual Total 2 17 19 SS M SF Significance F 0.063476954 0.031738 10.97144 0.000871318 0.049178046 0.002893 0.112655 Intercept SO/IP HR/IP Coefficients Standard Error Stat P-value Lower 95% Upper 95% 0.53650753 0.081408539 6.59031 4.59E-06 0.364750527 0.7082645 -0.2483475 0.071806578 -3.45856 0.003002 -0.39984616 -0.0968489 1.03193134 0.435884204 2.367444 0.030037 0.112296065 1.9515666 From the Excel output, the F-test statistics is 10.97 The p-value for this test is, From the Excel output, the p-value for this test is 0.0009

Decision The conclusion is that the p-value in this context is less than 0.05 which is 0.0009, so the null hypothesis is rejected at 5% level of significance. There is sufficient evidence to indicate that there is a significant overall relationship. The result is statistically significant

b) To test the hypothesis is that the slop of SO/IP is a significant factor at 5% significance level. The null and alternative hypothesis is, H:B, = 0 H.B.+0

The t-test statistics is, From the Excel output in part (a), the t-test statistics is - 3.46 The p-value for this test is, From the Excel output in part(a), the p-value for this test is 0.003

Decision The conclusion is that the p-value in this context is less than 0.05 which is 0.003, so the null hypothesis is rejected at 5% level of significance. There is sufficient evidence to indicate that the slop of SO/IP is a significant factor. The result is statistically significant.

To test the hypothesis is that the slop of HR/IP is a significant factor at 5% significance level. The null and alternative hypothesis is, H:B, = 0 H.B. 0

The t-test statistics is, From the Excel output in part (a), the t-test statistics is 2.37) The p-value for this test is, From the Excel output in part(a), the p-value for this test is 0.030.

Decision The conclusion is that the p-value in this context is less than 0.05 which is 0.030, so the null hypothesis is rejected at 5% level of significance. There is sufficient evidence to indicate that the slop of HR/IP is a significant factor. The result is statistically significant.