Assignment #4 Ch14, 15- QUESTION 5

2/14/24, 4:50 PM Assignment #4 Ch14, 15-Diatra Serra https://tdx.acs.pearsonprd.tech/api/v1/print/highered 1/6 Student: Diatra Serra Date: 02/14/24 Instructor: Victor Law Course: 202410 BUSN 3431 050 Assignment: Assignment #4 Ch14, 15 As a measure of productivity, a cell phone company records the number of customers each of its retail employees activates weekly. An activation is defined as either a new customer signing a cell phone contract or an existing customer renewing a contract. The accompanying table shows the number of weekly activations for eight randomly selected employees along with their job-satisfaction levels rated on a scale of 1-10 (10 Most satisfied). Complete parts a through d. = Click the icon to view the table showing and . 1 activations satisfaction a. Calculate the coefficient of determination. The coefficient of determination can be calculated using technology or the given formulas, where x and y are the sets of values for the independent and dependent variables, n is the number of ordered pairs, and are the predicted values. y , , and R 2 = SSR SST SSR = y − y 2 SST = y − 2 y 2 n While formulas or technology can be used to find the coefficient of determination, in this problem, Excel will be used. Copy the data and then paste the data into cell A1 of the spreadsheet, as shown. A B 1 Activations Satisfaction 2 32 8.0 3 24 7.9 4 42 8.5 5 38 9.0 • • • • • • • • • Use the Data Analysis Toolpack by selecting Data > Regression to open up the regression dialog box shown here . Select the appropriate ranges for the variables, including the labels. 2 Let satisfaction be the independent variable and let activations be the dependent variable. The input range for the x-values is and the input range for the y-values is B1:B9 A1:A9. Under Output Options , select Output Range and enter D1 in the corresponding input box. Be sure to check the Labels box and click OK to compute the regression results. The coefficient of determination is in the cell labeled R Square in the Regression Statistics part of the output. The result is , rounding to three decimal places. R 2 = 0.660 b. Using , test the significance of the population coefficient of determination. = 0.05 Begin by stating the hypotheses. The null hypothesis, , states the status quo. It is assumed to be true unless there is sufficient evidence to the contrary. The alternative hypothesis, , represents the opposite of the null hypothesis and is believed to be true if the null hypothesis is found to be false. H 0 H 1

2/14/24, 4:50 PM Assignment #4 Ch14, 15-Diatra Serra https://tdx.acs.pearsonprd.tech/api/v1/print/highered 2/6 In this situation, the test is a test to see if the coefficient of determination is zero. one tailed greater than The hypotheses for this test are H : = 0 and H : > 0. 0 2 1 2 The test statistic for the coefficient of determination can also be found in the regression output from Excel. It is located in the ANOVA part of the output in the column labeled F. R 2 Identify the F statistic from the Excel regression output shown here . 3 The test statistic is , rounding to two decimal places. F = 11.65 Identify the p-value for the statistic in the column labeled Significance F in the ANOVA part of the output. The p-value is , rounding to three decimal places. 0.014 Recall that the null hypothesis should be rejected if the p-value is less than . Otherwise, the null hypothesis should not be rejected. Therefore, at the level of significance, the null hypothesis. There sufficient evidence to conclude that the coefficient of determination is zero. 0.05 reject is greater than c. Construct a % confidence interval for the average number of activations made by an employee with a job-satisfaction score of . 90 8.4 The confidence interval for an average value of y is given by technology or the following formula, where the critical value comes from the Student's t-distribution with degrees of freedom and is the standard error of the estimate, where n is the number of ordered pairs, x is the set of values for the independent variable, is the sample mean of the x-values, and are the predicted values. t 2 n − 2 s e x y CI = ± t s y 2 e 1 n + x − x 2 x 2 − x 2 n Set up a part of the Excel worksheet to calculate the intermediate values. First, calculate the value for for a confidence level of %. 90 D E 20 x 8.4 21 Confidence level % 90 22 alpha 0.10 Use the formula to calculate the corresponding value for , rounding to two decimal places. = T.INV.2T(E22,6) t 2 D E 20 x 8.4 21 Confidence level % 90 22 alpha 0.10 = 1 − E21 23 Critical value 1.94 = T.INV.2T(E22,6)