Xander, summer statistics intern in the Superintendent’s Officefor the Palisades Point School District, wonders if the homerunteacher referrals in the 7th grade for two week periodsare comparable. He tests this claim very preliminarily at the 1%significance level as a pilot study, and presumes that thedistribution of referrals among these teachers is reasonablynormal. He collects independent, simple random samples. Thefollowing data tables represent the numbers of referrals made bythese seventh grade teachers:
Alcott | 10 | 15 | 23 | 20 | 18 | 16 | 20 | 20 | 16 | 18 |
Buck | 12 | 13 | 24 | 16 | 12 | 10 | 19 | 16 | 18 | |
Dickinson | 20 | 24 | 22 | 21 | 20 | 24 | 18 | | | |
Lee | 22 | 25 | 20 | 21 | 25 | 13 | 27 | 25 | | |
Oates | 25 | 18 | 26 | 23 | 32 | 16 | 20 | 23 | 24 | |
Walker | 16 | 18 | 20 | 12 | 16 | 18 | 20 | 12 | 14 | 17 |
What hypotheses should he test? Were the results statisticallysignificant? What conclusion should he draw, qualifying the resultas extreme or marginal if appropriate? Explain his anticipatedfindings in detail, both technically and contextually. Be sure toidentify the necessary critical and p-values as part of theanalysis.
