Stat 217 F2017 Assignment 3: Problem 12 Previous Problem Problem List Next Probl

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Stat 217 F2017 Assignment 3: Problem 12 Previous Problem Problem List Next Problem (1 point) Over his 20 season career in the NHL, Wayne Gretzky set virtually every significant career and single season scoring record. One record that did allude him was the record for most points in a single game. The record for most points in a single game is 10, which was done only once: Darryl Sittler set this record on February 7, 1976 against the Boston Bruins (He collected 6 goals and 4 assists.). Gretzky came close, amassing 8 points in a game twice in his career, both times in the 1983-1984 season. We will attempt to model Gretzky's points-per-game behaviour and from this, calculate the probability that he would at least tie the points in a game record. The data in the Minitab File contains a random sample of n = 100 games Gretzky played in from the 1981-82 season up to and including the 1985-86 season. For each game chosen, the number of points (goals assists) Gretzky scores was recorded. Note: You will need to tabulate this distribution in Minitab: Stat Tables.. (a) Use MINITAB to find the mean of this sample. Use two-decimals in your answer. X = 2.71 Test the hypothesis that the number of points Gretzky scored in a game (from 1981-82 to 1985-86) can be modeled by the Poisson distribution. Note: Use four-decimals in any probability calculations you need to make. (b) If the null hypothesis is true, how many of the games appearing in this sample would you expect Gretzky to score 4 points? Use two- decimals in your answer. Expected Number= (c) Find the value of the test statistic, using two decimals in your answer. Test Statistic

Explanation / Answer

(a) Here mean = 2.71

(B) We will use Chi-square test here so observed and expected table where

E(X) = POISSION (X; 2.71) * 100

E(4) = 100 * POISSION (4; 2.71) = 14.95

Here X2 = 3.9927

(d) P - value = 0.678

(c) Here we cannot reject the null hypothesis and can conclude that the data follow poisson distribution.

Gretzky data Count Expected (O-E)^2/E 0 6 6.65 0.0642 1 20 18.03 0.2149 2 18 24.43 1.6936 3 25 22.07 0.3888 4 19 14.95 1.0953 5 8 8.10 0.0013 6 4 5.75 0.5346 N 100 100 3.9927

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