In: Statistics and Probability
Xander, summer statistics intern in the Superintendent’s Office for the Palisades Point School District, wonders if the homerun teacher referrals in the 7th grade for two week periods are comparable. He tests this claim very preliminarily at the 1% significance level as a pilot study, and presumes that the distribution of referrals among these teachers is reasonably normal. He collects independent, simple random samples. The following data tables represent the numbers of referrals made by these 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 statistically significant? What conclusion should he draw, qualifying the result as extreme or marginal if appropriate? Explain his anticipated findings in detail, both technically and contextually. Be sure to identify the necessary critical and p-values as part of the analysis.