Exam 14: Categorical Data and Frequency Tables

A random sample of games was collected to determine if there is a difference in the population proportion of seven-game series won by the home team in several sports.The data appear in the contingency table. ​ ​ What is the expected count for the games won by the visiting team in baseball?

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.)

The target grade distribution for a particular course is 10% A, 30% B, 40% C, 15% D, 5% F.Students complain that a particular professor who teaches this course is much harder than others.They survey 152 former students of this professor's class and find they received the following grades: 10 A, 44 B, 64 C, 23 D, 11 F.Conduct a χ2 goodness-of-fit test to see if the data provide sufficient evidence to support the students' complaint.Select the appropriate critical value (CV), test statistic (TS), and decision.(Use α = 0.10.)