The Ugly Puddings, a hockey team of mathematicians who met back in graduate scho
ID: 3220347 • Letter: T
Question
The Ugly Puddings, a hockey team of mathematicians who met back in graduate school, are attempting to uncover the culprit behind their ongoing, season-long losing streak. Their coach claims that the players are "too smart" to score goals, i.e. their intellect causes them to overthink shooting the puck and thus they hit the goalie's pads directly or missing the net altogether. To refute the coach's claim, the team's goalie randomly samples 100 players from other teams in their league and classifies them according to their education level and number of goals scored this season. (a) State the goalie's null and alternate hypotheses. (b) Calculate the expected frequency for each combination of Education and Goals Scored. (c) Are the members of the Ugly Pucklings "too smart" to score goals, based on the data collected by the goalie, at a 95% confidence level?Explanation / Answer
H0 : Scoring goal is independent of their educational qualification.
H1 : Scoring goal is dependent on their educational qualification.
Goals scored
Education
0-1
2-5
Over 5
Total
High school
15
9
12
36
Undergraduate
14
11
10
35
Postgraduate
9
18
2
29
Total
38
38
24
100
Expected frequency:
E11 = 38*36/100 = 13.68 ~ 14
E12 = 38*36/100 = 13.68 ~ 14
E13 = 24*36/100 = 8.64 ~ 9
E21 = 38*35/100 = 13.30 ~ 13
E22 = 38*35/100 = 13.30 ~ 13
E23 = 24*35/100 = 8.4 ~ 8
E31 = 38*29/100 = 11.02~ 11
E32 = 38*29/100 = 11.02 ~ 11
E33 = 24*29/100 = 6.96 ~ 7
Goals scored
Education
0-1
2-5
Over 5
Total
High school
15 (14)
9(14)
12(9)
36
Undergraduate
14(13)
11(13)
10(8)
35
Postgraduate
9(11)
18(11)
2(7)
29
Total
38
38
24
100
2 = im jp (Oij – Eij)2 / Eij
where Oij is the observed frequency
Eij is the expected frequency
2 = 1/14 + 25/14 + 9/9 + 1/13 + 4/13 + 4/8 + 4/11 + 49/11 + 25/7 = 12.1313
df = (m-)(p-1) = 2*2= 4
= 0.05
20.05,4 = 9.488 ( from chi-square table)
Since 2cal = 12.13 > 2tab = 9.488, we reject the null hypothesis and conclude that Scoring goal is dependent on their educational qualification. Based on the data collected by the goalie, the members of the Ugly Pucklings “too smart” to score goals.
Goals scored
Education
0-1
2-5
Over 5
Total
High school
15
9
12
36
Undergraduate
14
11
10
35
Postgraduate
9
18
2
29
Total
38
38
24
100
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