Question

Is the difference between the mean annual salaries of statisticians in Region 1 and Region 2 more than 59000? To decide, you select a random sample of statisticians from each region. The results of each survey are shown to the night. At c = 0.10, what should you conclude? Region 1 X1 = $68,200 01 = $8750 n = 44 Region 2 X2 = $64,000 02 = $9150 m2 = 41 Click here to view page 1 of the standard normal distribution table, Click here to view page 2 of the standard normal distribution table, Choose the correct null and alternative hypotheses below. O A. Ho: 4-129000 H:H1-H2 = 9000 O D. Ho H1-H2 29000 Ha H1-H2 <9000 OB. Ho Hy-H2> 9000 Ha 11-42 S 9000 OE. HO H-H2> 9000 Ha H1-H229000 O C. Ho Hy- H2 = 9000 Ha 1-2 9000 OF. Ho H, H2 S 9000 HaH1-H2> 9000 Determine the critical value(s). (Round to two decimal places as needed. Use a com a to separate answers as needed.) Determine the rejection region. Select the correct choice below, and, if necessary, fill in any answer boxes to complete your choice. (Round to two decimal places as needed.) O A. z OR

Answer 1

Given that sample size n = 44, n = 41 The means #1 = 68200, 7 = 64000 standard deviation d = 8750, 0 = 9150 Null Hypothesis H, 44-47 9000 Alternative Hypothesis Ħ, : The difference between two region means is morethan $9000, 4-1 > 9000 (Right tail test) Option (F) is correct Level of significance a:= 10% = 0.1 for 10% LOS for right tail test from 2-table is 1.28 The critical value zo = 1.28 Rejection region : z>1.28 (71-73)-6 Test statistic: z= a. n, 68200-64000 := 2.1596 87502 91502 + 44 41 + Criterion: If zea <path, we accept the null hypothesis Otherwise we reject the null hypothesis. Conclusion: Since zcal = 2.1596 > 1.28 = Zpad Hence we reject the null hypothesis There is sufficient evidence to support the difference between the mean incomes is more tham 9000 Option (C) is correct