u...- The accompanying data are for each of two service stations operated by a national petroleum rener, which includes the daily sales in the convenience store located at the service station. The data for each day give the sales at the store (in dollars) and the number of gallons of gas sold. For both sites, the data covers 50 days. Complete parts (a) through (f) below. a Click the icon to view the data table. (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 trafc (as measured by the volume of gas sold)? Plotting sales versus volume shows that there V a correlation between these two variables and a comparison of the mean volumes for the two sites shows that they are |:| Volume is El to be a confounding variable in this analysis. (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. 0 H03P1=P2 O H03H17'P2 O H03P1ll2 Find the sample statistic for the difference of mean sales for the two sites, i1 - i2. Let sample 1 correspond to Site 1 and sample 2 correspond to Site 2. X1 ' x2 = '1 (Round to two decimal places as needed.) Determine the two-sample t-statistic. The t statistic is (Round to three decimal places as needed.) Sales (Dollars) 1980 2157 2347 2240 2798 2064 2328 2313 2531 2374 2610 2039 2030 2349 2428 2022 2055 2168 2535 2178 2422 2112 2192 2771 1898 1572 2282 2403 Volume (Gallons) 3834 3423 3698 3921 3779 2688 3918 3787 3886 3593 3724 2526 403 2383 3983 2370 3149 3913 4074 3638 4214 3997 3153 3808 2365 2575 3661 3505 Se Site 1 Se1 Site 1 Se1 Se1 Se1 Se1 Se1 Se1 Se1 Se1 Se1 Se1 Se1 Se1 Se1 Se1 Se1 Se1 Se1 Se1 Se1 Se1 Se1 Se1 Se1 Se1 Se1 Dummy 1 \\\\\\\\\\A\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\ Dummy * Volume I; full data set 3834 3423 3696 3921 3779 2666 3918 3767 3886 3593 3724 2526 403 2383 3983 2370 3149 3913 4074 3638 4214 3997 3153 3808 2365 2575 3661 3505 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. Reject the null hypothesis. The two-sample t-test finds a statistically significant difference, with Site 1 having more sales than Site 2. O B. 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. O C. Reject the null hypothesis. The two-sample t-test does not find a significant difference between the mean sales at the two sites. O D. 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 = ( + () Volume + () Dummy + () Dummy x Volume (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.Summarize the comparison of sales based on this analysis. Select the correct choice below and ll in any answer box within your choice. 0 A. For days of comparable volume, the sales at Site 1 are on average the same as the sales at Site 2. O 3- For days of comparable volume, the sales at Site 1 are on average $ 0 C. 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.) more than the sales at Site 2. (Round to three decimal places as needed.) (d) Compare the results from parts (b) and (0). 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% condence interval for the mean difference, :21 - i2, is from $ to $ more for Site El The condence interval from the regression is $ i values because the regression t V confounding due to volume. (e) Does the estimated multiple regression used in the analysis of covariance meet the similar variances condition? 0 A. The multiple regression does not meet the similar variances condition because the residuals are not nearly normal. 0 B. 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. 0 C. The multiple regression meets the similar variances condition. 0 D. The multiple regression does not meet the similar variances condition because the variation in the residuals changes as the tted values increase. to $ and generally contains (f) 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 volume is significant. O B. Yes, because the coefficients of the dummy variable and the interaction term are significant. O C. Yes, because the coefficient of the dummy variable is significant. O D. No, because all of the estimated parameters are significant