Sales (Dollars) Volume (Gallons) 1971 3828 2145 3410 2326 3657 2271 3945 2761 3821 2092 2671 2331 3958 2305 3804 2562 3841 2376 3597 2608 3736 2041 2558 1998 398 2345 2384 2473 3974 2030 2377 2033 3143 2203 3878 2519 4034 2183 3612 2416 4143 2104 3969 2179 3128 2816 3819 1902 2359 1591 2569 2304 3709 2358 3479 2942 4338 2530 3854 2747 3763 2093 3844 2170 3140 2179 3762 2242 3624 2485 3757 1837 2486 2426 4017 2485 3564 2555 3646 2258 3937 2976 4346 2048 1691 Site Site 1 Site 1 Site 1 Site 1 Site 1 Site 1 Site 1 Site 1 Site 1 Site 1 Site 1 Site 1 Site 1 Site 1 Site 1 Site 1 Site 1 Site 1 Site 1 Site 1 Site 1 Site 1 Site 1 Site 11 Site 1 Site 1 Site 1 Site 1 Site 1 Site 1 Site 1 Site 1 Site 1 Site 1 Site 1 Site 1 Site 1 Site 1 Site 1 Site 1 Site 1 Site 1 Site 1 Dummy 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Dummy Volur 3828 3410 3657 3945 3821 2671 3958 3804 3841 3597 3736 2558 398 2384 3974 2377 3143 3878 4034 3612 4143 3969 3128 3819 2359 2569 3709 3479 4338 3854 3763 3844 3140 3762 3624 3757 2486 4017 3564 3646 3937 4346 1691 2048 2405 2419 2340 1647 1498 2386 2172 1684 1697 1305 1657 1366 1448 1508 1661 1259 1186 1495 1424 1610 1844 1234 1221 1384 1301 1752 1176 1217 1607 1132 1380 1383 1670 1290 1475 1297 1663 1221 1297 1476 1545 1795 1775 1691 3710 3827 3302 1982 1843 3091 3127 2242 1623 1517 2502 2433 2696 2611 2673 2195 2040 2498 2554 2799 2602 2554 2526 2822 2615 2963 2318 2594 2612 1899 2174 2138 2442 2570 2644 2518 3263 2508 2169 2821 2856 2676 1560 Site 1 Site 1 Site 1 Site 1 Site 1 Site 1 Site 1 Site 1 Site 2 Site 2 Site 2 Site 2 Site 2 Site 2 Site 2 Site 2 Site 2 Site 2 Site 2 Site 2 Site 2 Site 2 Site 2 Site 2 Site 2 Site 2 Site 2 Site 2 Site 2 Site 2 Site 2 Site 2 Site 2 Site 2 Site 2 Site 2 Site 2 Site 2 Site 2 Site 2 Site 2 Site 2 Site 2 Site 2 1 1 1 1 1 1 ooooooooooooooooooooooooooo0000 1691 3710 3827 3302 1982 1843 3091 3127 0 oooooooooooooooooooooooooooooooooooo 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1775 1234 1286 1587 1533 1676 2265 1644 1851 2303 1309 1440 1468 1698 1785 1560 2526 2807 2602 2920 3089 2996 2822 3180 3037 1908 1902 2277 2564 2747 Site 2 Site 2 Site 2 Site 2 Site 2 Site 2 Site 2 Site 2 Site 2 Site 2 Site 2 Site 2 Site 2 Site 2 Site 2 OOOOOOOOOOOOOOO (a) Would it be appropriate for management of this chain of service stations to rate the operators of the convenience stores based on a two-sample comparison of the sales of the convenience stores during these two periods, or would such a comparison be confounded by different levels of traffic (as measured by the volume of gas solo Volume is to be a confounding variable in this analysis. Plotting sales versus volume shows that there a correlation between these two variables and a comparison of the mean volumes for the two sites shows that they are (b) Perform the two-sample t-test to compare the sales of the two service stations. Summarize this analysis, assuming that there are no lurking variables. State the null hypothesis for this test of hypothesis. O Ho: 1 O H:1 #11/ O Ho: 11 O H:1 =1 Find the sample statistic for the difference of mean sales for the two sites, X, -X. Let sample 1 correspond to Site 1 and sample 2 correspond to Site 2. x - x = (Round to two decimal places as needed.) Determine the two-sample t-statistic. The t statistic is (Round to three decimal places as needed.) Identify the p-value. The p-value is (Round to three decimal places as needed.) State the conclusion O A. Fail to reject the null hypothesis. The two-sample t-test finds a statistically significant difference, with Site 2 having more sales than Site 1. OB. Reject the null hypothesis. The two-sample t-test does not find a significant difference between the mean sales at the two sites. OC. Reject the null hypothesis. The two-sample t-test finds a statistically significant difference, with Site 1 having more sales than Site 2. OD. Fail to reject the null hypothesis. The two-sample t-test finds a statistically significant difference, with Site 1 mean sales about the same as Site 2 mean sales. (c) Compare the sales at the two sites using an analysis of covariance. Summarize the comparison of sales based on this analysis. Use a dummy variable coded as 1 for Site 1 and 0 otherwise. (Assume for the moment that the model meets the conditions for the MRM.) Determine the appropriate equation for the multiple regression. Use 0 for the coefficient of any regression parameter that should not be included in the regression equation. Estimated sales = (O+Volume + Dummy+ Dummy xVolume (Round to three decimal places as needed.) Summarize the comparison of sales based on this analysis. Select the correct choice below and fill in any answer box within your choice O A. For days of comparable volume, the sales at Site 1 are on average $ more than the sales at Site 2. (Round to three decimal places as needed.) O B. For days of comparable volume, the sales at Site 1 are on average the same as the sales at Site 2. OC. For days of comparable volume, the sales at Site 1 are on average $ less than the sales at Site 2. (Round to three decimal places as needed.) (d) Compare the results from parts (b) and (c). Do they agree? Explain why they agree or differ. Take into account the precision of the estimates and the answer to part (a). The 95% confidence interval for the mean difference, X4 - X2, is from $ to $more for Site The confidence interval from the regression is to $ and generally contains values because the regression fit confounding due to volume. (e) Does the estimated multiple regression used in the analysis of covariance meet the similar variances condition? O A. The multiple regression does not meet the similar variances condition because the residuals are not nearly normal. O B. The multiple regression does not meet the similar variances condition because the variation in the residuals changes as the fitted values increase. OC. The multiple regression does not meet the similar variances condition because the interquartile range of one site is more than twice that of the other site. OD. The multiple regression meets the similar variances condition. (1) Suppose an analyst fit the simple regression of sales in the convenience store on gas sales, ignoring the distinction between the two sites. Does this pooling of all the data together affect the relationship between sales in the store and gas sales? O A. Yes, because the coefficient of the dummy variable is significant O B. Yes, because the coefficients of the dummy variable and the interaction term are significant OC. No, because all of the estimated parameters are significant OD. Yes, because the coefficient of volume is significant. Sales (Dollars) Volume (Gallons) 1971 3828 2145 3410 2326 3657 2271 3945 2761 3821 2092 2671 2331 3958 2305 3804 2562 3841 2376 3597 2608 3736 2041 2558 1998 398 2345 2384 2473 3974 2030 2377 2033 3143 2203 3878 2519 4034 2183 3612 2416 4143 2104 3969 2179 3128 2816 3819 1902 2359 1591 2569 2304 3709 2358 3479 2942 4338 2530 3854 2747 3763 2093 3844 2170 3140 2179 3762 2242 3624 2485 3757 1837 2486 2426 4017 2485 3564 2555 3646 2258 3937 2976 4346 2048 1691 Site Site 1 Site 1 Site 1 Site 1 Site 1 Site 1 Site 1 Site 1 Site 1 Site 1 Site 1 Site 1 Site 1 Site 1 Site 1 Site 1 Site 1 Site 1 Site 1 Site 1 Site 1 Site 1 Site 1 Site 11 Site 1 Site 1 Site 1 Site 1 Site 1 Site 1 Site 1 Site 1 Site 1 Site 1 Site 1 Site 1 Site 1 Site 1 Site 1 Site 1 Site 1 Site 1 Site 1 Dummy 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Dummy Volur 3828 3410 3657 3945 3821 2671 3958 3804 3841 3597 3736 2558 398 2384 3974 2377 3143 3878 4034 3612 4143 3969 3128 3819 2359 2569 3709 3479 4338 3854 3763 3844 3140 3762 3624 3757 2486 4017 3564 3646 3937 4346 1691 2048 2405 2419 2340 1647 1498 2386 2172 1684 1697 1305 1657 1366 1448 1508 1661 1259 1186 1495 1424 1610 1844 1234 1221 1384 1301 1752 1176 1217 1607 1132 1380 1383 1670 1290 1475 1297 1663 1221 1297 1476 1545 1795 1775 1691 3710 3827 3302 1982 1843 3091 3127 2242 1623 1517 2502 2433 2696 2611 2673 2195 2040 2498 2554 2799 2602 2554 2526 2822 2615 2963 2318 2594 2612 1899 2174 2138 2442 2570 2644 2518 3263 2508 2169 2821 2856 2676 1560 Site 1 Site 1 Site 1 Site 1 Site 1 Site 1 Site 1 Site 1 Site 2 Site 2 Site 2 Site 2 Site 2 Site 2 Site 2 Site 2 Site 2 Site 2 Site 2 Site 2 Site 2 Site 2 Site 2 Site 2 Site 2 Site 2 Site 2 Site 2 Site 2 Site 2 Site 2 Site 2 Site 2 Site 2 Site 2 Site 2 Site 2 Site 2 Site 2 Site 2 Site 2 Site 2 Site 2 Site 2 1 1 1 1 1 1 ooooooooooooooooooooooooooo0000 1691 3710 3827 3302 1982 1843 3091 3127 0 oooooooooooooooooooooooooooooooooooo 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1775 1234 1286 1587 1533 1676 2265 1644 1851 2303 1309 1440 1468 1698 1785 1560 2526 2807 2602 2920 3089 2996 2822 3180 3037 1908 1902 2277 2564 2747 Site 2 Site 2 Site 2 Site 2 Site 2 Site 2 Site 2 Site 2 Site 2 Site 2 Site 2 Site 2 Site 2 Site 2 Site 2 OOOOOOOOOOOOOOO (a) Would it be appropriate for management of this chain of service stations to rate the operators of the convenience stores based on a two-sample comparison of the sales of the convenience stores during these two periods, or would such a comparison be confounded by different levels of traffic (as measured by the volume of gas solo Volume is to be a confounding variable in this analysis. Plotting sales versus volume shows that there a correlation between these two variables and a comparison of the mean volumes for the two sites shows that they are (b) Perform the two-sample t-test to compare the sales of the two service stations. Summarize this analysis, assuming that there are no lurking variables. State the null hypothesis for this test of hypothesis. O Ho: 1 O H:1 #11/ O Ho: 11 O H:1 =1 Find the sample statistic for the difference of mean sales for the two sites, X, -X. Let sample 1 correspond to Site 1 and sample 2 correspond to Site 2. x - x = (Round to two decimal places as needed.) Determine the two-sample t-statistic. The t statistic is (Round to three decimal places as needed.) Identify the p-value. The p-value is (Round to three decimal places as needed.) State the conclusion O A. Fail to reject the null hypothesis. The two-sample t-test finds a statistically significant difference, with Site 2 having more sales than Site 1. OB. Reject the null hypothesis. The two-sample t-test does not find a significant difference between the mean sales at the two sites. OC. Reject the null hypothesis. The two-sample t-test finds a statistically significant difference, with Site 1 having more sales than Site 2. OD. Fail to reject the null hypothesis. The two-sample t-test finds a statistically significant difference, with Site 1 mean sales about the same as Site 2 mean sales. (c) Compare the sales at the two sites using an analysis of covariance. Summarize the comparison of sales based on this analysis. Use a dummy variable coded as 1 for Site 1 and 0 otherwise. (Assume for the moment that the model meets the conditions for the MRM.) Determine the appropriate equation for the multiple regression. Use 0 for the coefficient of any regression parameter that should not be included in the regression equation. Estimated sales = (O+Volume + Dummy+ Dummy xVolume (Round to three decimal places as needed.) Summarize the comparison of sales based on this analysis. Select the correct choice below and fill in any answer box within your choice O A. For days of comparable volume, the sales at Site 1 are on average $ more than the sales at Site 2. (Round to three decimal places as needed.) O B. For days of comparable volume, the sales at Site 1 are on average the same as the sales at Site 2. OC. For days of comparable volume, the sales at Site 1 are on average $ less than the sales at Site 2. (Round to three decimal places as needed.) (d) Compare the results from parts (b) and (c). Do they agree? Explain why they agree or differ. Take into account the precision of the estimates and the answer to part (a). The 95% confidence interval for the mean difference, X4 - X2, is from $ to $more for Site The confidence interval from the regression is to $ and generally contains values because the regression fit confounding due to volume. (e) Does the estimated multiple regression used in the analysis of covariance meet the similar variances condition? O A. The multiple regression does not meet the similar variances condition because the residuals are not nearly normal. O B. The multiple regression does not meet the similar variances condition because the variation in the residuals changes as the fitted values increase. OC. The multiple regression does not meet the similar variances condition because the interquartile range of one site is more than twice that of the other site. OD. The multiple regression meets the similar variances condition. (1) Suppose an analyst fit the simple regression of sales in the convenience store on gas sales, ignoring the distinction between the two sites. Does this pooling of all the data together affect the relationship between sales in the store and gas sales? O A. Yes, because the coefficient of the dummy variable is significant O B. Yes, because the coefficients of the dummy variable and the interaction term are significant OC. No, because all of the estimated parameters are significant OD. Yes, because the coefficient of volume is significant