Heights of children who repeat grades. 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 to those who did not (Archives of Disease in Childhood, April 2000). All height measurements were standardized using z-scores. A summary of the results, by gender, is shown in the table.
(a) Conduct a test of hypothesis to determine whether the average height of Australian boys who repeated a grade is less than the average height of boys who never repeated. Use α = .05.
(b) Repeat part a for Australian girls.
(c) Summarize the results of the hypothesis tests in the words of the problem.
Source: Reproduced from Archives of Disease in Childhood, ‘‘Does height influence progression through primary school grades?" Melissa Wake, David Coghlan, and Kylie Hesketh, Vol. 82, Issue 4, April 2000 (Table 3), with permission from BMJ Publishing Group Ltd.