The management of a large firm would like to know something about employee morale and the other variables to which it may be related. To study these relationships, each employee in a simple random sample of 33 amy is interviewed and tested to obtain information concerning morale level and the average number of satisfying extra work social contacts experienced during a week. Whether or not the duties the employee usually performs are appropriate to the job title is also determined. The part of results is shown in the following table. Measure of morale Average number of social Duties agree with job title? Y contacts: X1 X2 795 13 Yes 1593 16 No The dependent variable Y is measure of morale, the quantitative independent variable, X1 is average number of social contacts, and the following dummy variable coding is used to quantify the qualitative variable: X2 = 1 if yes, X2 = 0 it no. The model including dummy variable and the interaction term was being estimated and a part of computer outputs is below: beta std error t p-value 95% CI for B Lower bound Upper bound (Constant) 175 134.308 X1 45 5.427 X2 -85 35.211 X1X2 32.927 8.315 n 33 F P-value SSE 198542 3535235393 SSR 542888 Note: SSE = $5 Explained. 35R = SS Residuals a. Write an appropriate multiple population regression model. b. What is the expected measure oi morale if the average number of social contacts is 15 and the duties agree with job title is Yes? c. What is the expected measure of morale if the average number of social contacts is 15 and the duties agree with job title is No? d. You are to conduct tests of hypotheses to determine if variable X1 is significant. Use alpha = 8.05. 1} State the null and alternative hypothesis. 2} Compute the test statistic. 3} State the critical value and show the rejection region graphically. 4) State the conclusion. Is it significant