An NFL team is getting ready to face its next opponent.In games over the last two seasons, this opponent ran the ball 60% of the time, passed the ball 38% of the time, and did some form of trick play 2% of the time (ignoring plays by special teams).Sports analysts believe that due to some coaching philosophy adjustments, the opponent's distribution of plays has changed this season.In this season's games, the team has run 252 offensive plays (again, ignoring special teams plays): 125 were running plays, 123 were pass plays, and 4 were trick plays.Conduct a χ2 goodness-of-fit test to see if the data provide sufficient evidence to conclude the play percentages have changed this year as compared to the previous two years.Select the appropriate critical value (CV), test statistic (TS), and decision.(Use α = 0.01.)
A) CV = 9.2103, TS = 12.5033, reject H₀
B) CV = 9.2103, TS = 349.8375, reject H₀
C) CV = 4.6052, TS = 12.5033, reject H₀
D) CV = 11.3449, TS = 349.8375, reject H₀

Question

Quizplus · Accepted Answer

CV = 9.2103, TS = 12.5033, reject H₀The correct critical value for a χ2 test with 2 degrees of freedom at α = 0.01 is 9.2103. The test statistic calculated from the observed and expected frequencies (based on the percentages given for the previous seasons) indicates a significant difference, leading to the rejection of the null hypothesis that the play distribution has not changed.

An NFL Team Is Getting Ready to Face Its Next