Printouts for PART C One-way ANOVA: engagement versus rewards Source rewards Error Total DF 4 95 99 S = 0.8255 Level 1 2 3 4 5 N 20 20 20 20 20 SS 179.489 64.739 244.227 MS 44.872 0.681 R-Sq = 73.49% Mean 1.1307 2.6726 3.8115 4.3607 4.8857 StDev 0.6377 0.7563 0.8864 0.8455 0.9634 F 65.85 P 0.000 R-Sq(adj) = 72.38% Individual 95% CIs For Mean Based on Pooled StDev ----+---------+---------+---------+----(--*--) (--*--) (--*--) (--*--) (--*--) ----+---------+---------+---------+----1.2 2.4 3.6 4.8 Pooled StDev = 0.8255 Tukey 95% Simultaneous Confidence Intervals All Pairwise Comparisons among Levels of rewards Individual confidence level = 99.34% rewards = 1 subtracted from: rewards 2 3 4 5 Lower 0.8165 1.9553 2.5045 3.0296 Center 1.5419 2.6808 3.2300 3.7550 Upper 2.2674 3.4062 3.9554 4.4804 -----+---------+---------+---------+---(---*--) (--*---) (--*---) (---*--) -----+---------+---------+---------+----2.0 0.0 2.0 4.0 rewards = 2 subtracted from: rewards 3 4 5 Lower 0.4134 0.9626 1.4876 Center 1.1388 1.6880 2.2131 Upper 1.8643 2.4135 2.9385 -----+---------+---------+---------+---(---*--) (--*---) (---*---) -----+---------+---------+---------+----2.0 0.0 2.0 4.0 rewards = 3 subtracted from: rewards 4 5 Lower -0.1762 0.3488 Center 0.5492 1.0742 Upper 1.2746 1.7997 -----+---------+---------+---------+---(---*--) (--*---) -----+---------+---------+---------+----2.0 0.0 2.0 4.0 rewards = 4 subtracted from: rewards 5 Lower -0.2004 Center 0.5250 Upper 1.2504 -----+---------+---------+---------+---(---*--) -----+---------+---------+---------+----2.0 0.0 2.0 4.0 30 PART C. [20 points] A consultant in human resource management is studying the relationship between compensation and engagement among employees at a large corporation. The consultant identifies five levels of compensation (labeled 1,2,,5 , with 1 being the lowest level of compensation and 5 being the highest) and has developed a scale to measure employee engagement. The printout shows a one-way ANOVA based on data the consultant collects. Let 1,, 5 be the population means of the engagement scores for the five levels of compensation. 1. [1 point] How many employees are sampled at each level of compensation? 1 2. [1 point] Give the estimate of 3 , the population mean engagement score for compensation level 3 . 3. [1 point] Give the estimate of the standard deviation of the population of engagement scores for compensation level 3 . 4. [2 points] What is the null hypothesis being tested in the ANOVA table? 5. [2 points] What is the alternative hypothesis for the test in the ANOVA table? 6. [2 points] What distribution is used for computing the p value in the ANOVA table? 7. [2 points] Is the null hypothesis tested in the ANOVA table rejected in a test at the 5% level? 2 8. [3 points] Give a 95% confidence interval for 5 . 9. [1 point] Give the estimate of the difference in population means of the engagement score between compensation level 4 and compensation level 1, i.e., give the estimate of 4 1. 10. [5 points] What can you conclude about the ordering of the means 1,, 5 based on the Tukey simultaneous confidence intervals? 3