a. Show that it is appropriate to carry out a chi-square test using expected frequencies obtained. b. Test the null versus alternative hypothesis at the .05 level of significance by comparing the Chi-Square Goodness-of-Fit Statistic obtained with the critical chi-square statistic from the table. Find the critical chi-square statistic in the table for the degrees of freedom of = (number of categories - 1). c. Using p-value to test the hypothesis: Use the Chi-Square Goodness-of-Fit Statistic obtained to find the corresponding p-value Click on an empty cell, say cell G10, and select the Insert Function button on the Excel ribbon. In the Insert Function dialog box, select Statistical from the "Or select a category:" menu, select CHISQ. DIST.RT (Chi Distribution Right Tail) from the "Select a function:" menu, and click OK. In the "CHISQ.DIST.RT Function Arguments" dialog box, enter the cell with Chi-Square Goodness-of-Fit test statistic value into the "X" window, enter your df into the "Deg_freedom" window. Click OK in the "CHISQ.DIST.RT Function Arguments" dialog box. The right tail area related to the value of the chi-square statistic will be produced. Use the p-value obtained to test your hypothesis by comparing the p-value with a = .05. d. What do you conclude about the difference between the error percentages for the computerized system and the manual system?Computerized Manual Observed Expected Frequencies, Frequencies, Previous Errors Probabilities, EEnp (f-E) (f-E)^2 (f-E)^2/E 479 10.87 435 44 1936 4.450574713 1 10 0.08 40 -30 900 22.5 2 0.03 15 49 3.266666667 3 2 0.01 5 -3 1.8 >3 0.01 16 3.2 Total 500 500 2910 35.21724138After performing chi-square test, if you rejected the null hypothesis, you may find the Confidence Interval for the proportion of interest by using the method we studied in Stats 1 course p(1 - p ) [p + Zxx/2 na. Find 95% Confidence Interval for the mean proportion of not having errors for the new computerized invoicing system. The sample proportion / in the formula above may be found as a ratio of the corresponding observed frequency and the total number of observations /. b. What does the confidence interval say