The effect of bank size Table 10.1 gives the wages and months of service for a sample of 59 married women who hold customer service jobs in Indiana banks. The table also notes whether each woman worked at a large bank (100 or more workers) or at a smaller bank. This data is available in a Minitab project, L4HW3. Question 11 pts Figure 10.3 is a scatterplot of wages against length of service for all 59 women. Shown below is a new scatterplot of these variables using different symbols for the 34 women who work in large banks (red mark) and the 25 women who work in small banks (blue mark): Let us denote the group of the 34 women who work in large banks by "1", and the group of the 25 women who work in small banks by "2". Fill in the blank: The group number for which it appears that regressing wages on length of service will do a better job of explaining wages is: _______ . Group 1 Group 2 Question 21 pts Suppose we wanted to compare mean wages at small and at large banks. Specifically, we wanted to test the null hypothesis that the average wage at small banks is equal to the average wage at large banks. What method could we use to test this hypothesis? ANOVA Two-sample t-test Chi-square analysis Z-test for two proportions Question 32 pts The plot in the previous exercise seems to indicate that bank size does influence the relationship between wages and length of service. Do separate regressions of wages on length of service for large banks (n = 34) and for small banks (n = 25). Give the equation of the regression line of wages on length of service for large banks. Give your answers as presented by Minitab. The intercept of the regression line is (give your answer to 1 decimal places): The slope of the regression line is (give your answer to 3 decimal places): $/LOS. Question 4 1 pts If we wish to test the significance of the coefficient on years of service, which is the appropriate null hypothesis? =. 425 =0 0 Question 5 2 pts We can test the significance of the regression coefficient using a tstatistic. For the large firms, the t statistic is and its pvalue is Use 2 decimal places. Question 6 1 pts For the large banks, what conclusion do we reach? We reject the null hypothesis and conclude that the coefficient is significant. We reject the null hypothesis and conclude that the coefficient is NOT significant. We fail to reject the null hypothesis and conclude that the coefficient is significant. We fail to reject the null hypothesis and conclude that the coefficient is NOT significant. Question 7 2 pts The plot and tests of the previous exercises seem to confirm that bank size does influence the relationship between wages and length of service. Do separate regressions of wages on length of service for large banks (n = 34) and for small banks (n = 25). You need to separate the data into two subsets, one for large banks and one for small banks. First, consider the SMALL banks. The intercept of the regression line is (give your answer to 1 decimal places): The slope of the regression line is (give your answers to 3 decimal places): $/LOS Question 8 2 pts For the small firms, report the tstatistic for the test of the significance of the coefficient and its pvalue Use 2 decimal places. Question 9 1 pts What conclusion do we reach for small banks? We reject the null hypothesis and conclude that the coefficient is significant. We reject the null hypothesis and conclude that the coefficient is NOT significant. We fail to reject the null hypothesis and conclude that the coefficient is significant. We fail to reject the null hypothesis and conclude that the coefficient is NOT significant. Question 10 1 pts Let us denote the group of the 34 women who work in large banks by "1", and the group of the 25 women who work in small banks by "2". Fill in the blank: The group number for which we might use, according to the significance tests, the length of service to predict wages is: _______ . 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Question 11 pts Figure 10.3 is a scatterplot of wages against length of service for all 59 women. Shown below is a new scatterplot of these variables using different symbols for the 34 women who work in large banks (red mark) and the 25 women who work in small banks (blue mark): Let us denote the group of the 34 women who work in large banks by "1", and the group of the 25 women who work in small banks by "2". Fill in the blank: The group number for which it appears that regressing wages on length of service will do a better job of explaining wages is: _______ . Group 1 Group 2 Question 21 pts Suppose we wanted to compare mean wages at small and at large banks. Specifically, we wanted to test the null hypothesis that the average wage at small banks is equal to the average wage at large banks. What method could we use to test this hypothesis? ANOVA Two-sample t-test Chi-square analysis Z-test for two proportions Question 32 pts The plot in the previous exercise seems to indicate that bank size does influence the relationship between wages and length of service. Do separate regressions of wages on length of service for large banks (n = 34) and for small banks (n = 25). Give the equation of the regression line of wages on length of service for large banks. Give your answers as presented by Minitab. The intercept of the regression line is (give your answer to 1 decimal places): 390.2 The slope of the regression line is (give your answer to 3 decimal places): 0.425 $/LOS. Question 4 1 pts If we wish to test the significance of the coefficient on years of service, which is the appropriate null hypothesis? = .425 =0 0 Question 5 2 pts We can test the significance of the regression coefficient using a tstatistic. For the large firms, the t statistic is 1.27 and its pvalue is 0.21 Use 2 decimal places. Question 6 1 pts For the large banks, what conclusion do we reach? We reject the null hypothesis and conclude that the coefficient is significant. We reject the null hypothesis and conclude that the coefficient is NOT significant. We fail to reject the null hypothesis and conclude that the coefficient is significant. We fail to reject the null hypothesis and conclude that the coefficient is NOT significant. Question 7 2 pts The plot and tests of the previous exercises seem to confirm that bank size does influence the relationship between wages and length of service. Do separate regressions of wages on length of service for large banks (n = 34) and for small banks (n = 25). You need to separate the data into two subsets, one for large banks and one for small banks. First, consider the SMALL banks. The intercept of the regression line is (give your answer to 1 decimal places): 289.2 The slope of the regression line is (give your answers to 3 decimal places): 0.841 $/LOS Question 8 2 pts For the small firms, report the tstatistic for the test of the significance of the coefficient 4.49 and its pvalue 0.00 Use 2 decimal places. Question 9 1 pts What conclusion do we reach for small banks? We reject the null hypothesis and conclude that the coefficient is significant. We reject the null hypothesis and conclude that the coefficient is NOT significant. We fail to reject the null hypothesis and conclude that the coefficient is significant. We fail to reject the null hypothesis and conclude that the coefficient is NOT significant. Question 10 1 pts Let us denote the group of the 34 women who work in large banks by "1", and the group of the 25 women who work in small banks by "2". Fill in the blank: The group number for which we might use, according to the significance tests, the length of service to predict wages is: _______ . Group 1 Group 2