The Ugly Pucklings, a hockey team of mathematicians who met back in graduate sch

Question

The Ugly Pucklings, 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

here null hypothesis: education level and goals scored are independent to each other.

alternate hypothesis:education level and goals scored are dependent to each other.

b)

c) for above test stat 12.101 ; at 4 degree of freedom p value =0.0166

as p value is less then 0.05 we reject null hypothesis and conclude that goals and education level are dependent.

Observed O 0-1 2-5' >5 Total High school 15 9 12 36 Undergraduate 14 11 10 35 Post graduate 9 18 2 29 Total 38 38 24 100 Expected E=rowtotal*column total/grand total 0-1 2-5' >5 Total High school 13.680 13.680 8.640 36 Undergraduate 13.300 13.300 8.400 35 Post graduate 11.020 11.020 6.960 29 Total 38 38 24 100 chi square =(O-E)^2/E 0-1 2-5' >5 Total High school 0.127 1.601 1.307 3.035 Undergraduate 0.037 0.398 0.305 0.739 Post graduate 0.370 4.421 3.535 8.326 Total 0.534 6.420 5.146 12.101

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