Heights of grade school repeaters. Are children who repeat a grade in elementary school sh...

Heights of grade school repeaters. Are children who repeat a grade in elementary school shorter, on average, than their peers? To answer this question, researchers compared the heights of Australian schoolchildren who repeated a grade with the heights of those who did not ( Archives of Disease in Childhood , Apr. 2000). All height measurements were standardized with the use of z -scores. A summary of the results, by gender, is shown in the following table:

a. Set up the null and alternative hypothesis for determining whether the average height of Australian boys who repeated a grade is less than the average height of boys who never repeated.

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b. Conduct the test you set up in part a, using α = .05.

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c. Repeat parts a and b for Australian girls.

*d. Within each grade, the children were divided into equal thirds (tertiles) based on age (youngest third, middle third, and oldest third). The researchers also compared the average heights of the three groups using an ANOVA. For boys, the F-test resulted in p-value=.01. Interpret the results at  α = .05.