Help with the following. Use the last two images (images 3 and 4) to help with the pre-activity.

4-6 ONE-WAY ANALYSIS OF VARIANCE (ANOVA) PRE-ACTIVITY Eighty new hires were randomly assigned to one of four training programs, then given a com- petency test upon completion. A researcher plans to do a 1-way ANOVA to compare mean competency test scores. 1. a. The research question is The population of interest is and the sample is . The explanatory variable is which is (circle one) quantitative categorical, and the response variable which is (circle one) quantitative categorical. b. Is this study an observational study or an experiment? Explain why. 2. The ANOVA test discussed in this section has conditions similar to those of prior inference procedures. The conditions under which a 1-way ANOVA can be used are as follows: All observations must be independently selected (random sampling from groups or random assignment to groups). Population sizes must be at least 10 times sample sizes All groups must be approximately normally distributed with similar variances (largest standard deviation no more than twice smallest standard deviation), similar sample sizes, and no outliers. Alpha Bravo Charlie Delta Frequency Frequency Frequency Frequency 1 2 5 1 2 3 4 5 6 456789 1 2 3 4 5 6 a. For the similar variances requirement, explain how you could use graphs to estimate whether this condition is met. Learning Through Practice: Statistical Reasoning 1671 . a. The research question is Did the new hires complete their job training? Do different training programs result in different competency test scores? Are these new hires competent at their jobs? What is the average competency test score for a new hire? The population of interest is The 80 new hires in the study New hires at this company Job training programs The 4 job training programs in the study The sample is The 80 new hires in the study New hires at this company The 4 job training programs in the study Job training programs The explanatory variable is Did they get hired? Which new hire was it? Which training program were they assigned? Competency test score which is Quantitative CategoricalThe response variable is Which training program were they assigned? Competency test score Did they get hired? Which new hire was it? which is Quantitative Categorical b. Is this study an observational study or an experiment? Observational study Experiment 2. a. Is the similar variances requirement met? No, the values in all 4 data sets are similarly spread out. No, the Charlie data set tends to have higher values than the other data sets. Yes b. Do the conditions for ANOVA appear to be met? No, a sample size of 80 is not large enough. Yes No, the sample is not random. No, the Charlie data set is an outlier. 3. Do the side by side boxplots appear to support the null or alternative hypothesis? The alternative hypothesis, it appears that the average scores for the four different trainings are similar. The null hypothesis, it appears that new hires who received the Charlie training tend to score higher on average than new hires who received one of the other three trainings. The alternative hypothesis, it appears that new hires who received the Charlie training tend to score higher on average than new hires who received one of the other three trainings. The null hypothesis, it appears that the average scores for the four different trainings are similar.4-6 One-Way Analysis of Variance (ANOVA): Pre-Activity b. Do conditions for an ANOVA appear to be met? Explain. Competency Scores after Job Training O Delta Alpha Bravo Charlie 3. Do the side by side boxplots for the data from the four groups appear to support the null or alternative hypothesis (see the end of the Getting Started section)? Explain. How far apart do group means have to be in comparison to the variation within each group to reject the null hypothesis and conclude the means differ? The ANOVA uses an F-test statistic to compare variances and answer this question. 168 Learni