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# C state a null and an alternative hypothesis to

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(c) State a null and an alternative hypothesis to reflect the researchers’ conjecture. Null hypothesis: Alternative hypothesis: (d) Explain what a Type I error and a Type II error represent in this context. Type I error: Type II error: (e) Consider the following sets of boxplots. What is the same and what is different about the distributions displayed by these boxplots? In which group do you believe the evidence will be stronger that at least one population mean differs from the others? Explain. A: B: Same: Different: Stronger evidence (A or B): Explain:

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Chance/Rossman, 2015 ISCAM III Investigation 5.4 339 Discussion: In the above boxplots, the sample mean scores are roughly the same for graphs A and B (6.2, 4.4, 7.1, 3.1, 7.0)), but the variability within each group is much larger for the distributions in graph A. This larger amount of “within - sample” variation makes the difference s in sample means seem not as extreme compared to graph B. Graph B displays less within-sample variability and so the differences in the sample means appear more extreme and provide more evidence that the crutches scores and the hearing scores did not come from the same population with the same population mean. So, our goal in comparing the sample means will be to decide whether the differences in the sample means are larger than what we would expect by random chance, where the amount of within-sample variation will give us an indication as how much we expect the response values to vary “by chance.” (f) The actual data are stored in DisabilityEmployment.txt . Produce parallel boxplots and descriptive statistics of the qualification scores among the five groups. Record the descriptive statistics in the table below. None Amputee Crutches Hearing Wheelchair Sample size Sample mean Sample std. dev. Do these data suggest evidence of a difference among the population means? Write a paragraph supporting your statements. Just as the chi-square test statistic provides a single number to compare how different sample proportions are across several groups, we need a test statistic that simultaneously measures the differences in sample means among several groups. As noted above, we will do this by considering the variation in the sample means from the overall mean, and assessing whether that variation is much larger than would be expected based on the chance variation exhibited within the samples. (See the Applet Exploration to explore another possible statistic.) (g) What is the overall mean applicant qualification rating assigned by the 70 students? (h) If we were to treat the five sample means as five observations, calculate the standard deviation of these five values. Then square the standard deviation to calculate the variance . (i) Is it reasonable to allow each of these sample means to have the same relative contribution to our overall measure of variability between group means? Explain.
Chance/Rossman, 2015 ISCAM III Investigation 5.4 340 Our measure of the variability between groups or “treatment effect” will be the weighted variance across the groups where the weights are the sample sizes.

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