Question

8 plant wants to determine whether the mean manager performance ratings ed over the past month. The table shows the plant's perfomance ratings for 3. A manufacturing want the same six managers last month an d this month. 6 78 89 5 81 92 4 76 86 Manager Number1 Rating (last month) 85 Rating (this month) 88 2 96 85 70 89 Sample standard deviation Summary Statistics Rating (last month) Rating (this month) Difference Mean 81.00 88.17 8.90 2.48 10.24 At a level of significance equal to 0.05, is there enough evidence to conclude that the mean performance rating has changed over the past month? Assume that the sample data meet the conditions required to use the Central Limit Theorem to estimate the value of the standard error for the appropriate test (a) State the null and alternative hypotheses. (b) Calculate the t-statistic and estimate the p-value. (c) Interpret the results with respect to the null hypothesis. Explain what they mean: how does mean manager performance this month compare to performance for last month?

Answer 1

Given data is 7.17 μ,- 여 =>(474)2=10.242 10.24 a) Null Hypothesis Ho: μ,-0 Alternative Hypothesis: <0 (Left tail test)) b)The best estimator is t= -07.17-0 10.24.7-=-1.715 The test statistic t=-1.715 c)The level of significance is α-590-0.05 ts/ with n-1 = 6-1 = 5 degrees of freed n is-2.57 p-Value: F(-1.715)-F(-2.57) F(2.57)-F(1.72) = 0.9959-0.9573 = 0.0386 Conclusion: Since p-Value <0.05 (LOS) We accept the null hypothesis There is no difference in ranks before and after. (ie) Vo improvem