A random sample of 1,348 people was selected from the fans that attended the IU
ID: 3207620 • Letter: A
Question
A random sample of 1,348 people was selected from the fans that attended the IU vs. KY NCAA basketball game in 2014. The sample was made up of 890 men and 458 women who were asked if they enjoyed watching the game. Seventy-seven percent of the men enjoyed watching the game, and 35% of the women enjoyed watching the game. Construct a 2 X 2 contingency table. Show all work! (15 pts) a). If one respondent is chosen at random, what is the probability that it is a man who didn’t enjoy watching the game? b). If one respondent is chosen at random, what is the probability that it is a woman who enjoyed watching the game? c). Suppose the respondent chosen is a female. What, then, is the probability that she did not enjoy watching the game? d). Suppose the respondent chosen enjoyed watching the game. What, then, is the probability that the individual is a male? e). Is enjoying watching the game and the gender of the individual statistically independent? Explain.
Explanation / Answer
No of men that are sampled = 890
No. of women that are sampled = 458
77% of men enjoyed watching the game.
No. of men enjoyed watching the game = 77% of 890 = 890 x 0.77 = 685.3 =685
No. men did not enjoy watching the game = 890 - 685 = 205
35% of women enjoyed watching the game
No. Women enjoyed watching the game = 35 % of 458 = 458 x 0.35 = 160
No. Women did not enjoy watching the game = 458 - 160 = 298
2 x 2 contingency table
a). If one respondent is chosen at random, what is the probability that it is a man who didn’t enjoy watching the game?
If one respondent is chosen at random,
Probability that it is a man who didn’t enjoy watching the game = No. of men who did not enjoy watching the game/Total no. of respondents
From the above table ,
No. of men who did not enjoy watching the game =205
Total no. of respondents = 1348
If one respondent is chosen at random,
Probability that it is a man who didn’t enjoy watching the game = 205/1348 = 0.1521
b). If one respondent is chosen at random, what is the probability that it is a woman who enjoyed watching the game?
If one respondent is chosen at random,
Probability that it is a woman who enjoyed watching the game = No. of women who enjoyed watching the game/Total no. of respondents
From the above table ,
No. of women who enjoyed watching the game =160
Total no. of respondents = 1348
If one respondent is chosen at random
Probability that it is a woman who enjoyed watching the game = 160/1348 = 0.1187
c). Suppose the respondent chosen is a female. What, then, is the probability that she did not enjoy watching the game?
Given that the respondent chosen is female,
Probability that she did not enjoy watching the game = No. of women who did not enjoy watching the game/Total no. of women respondents
From the above table ,
No. of women who did not enjoy watching the game =298
Total no. of women respondents = 458
Given that the respondent chosen is female,
Probability that she did not enjoy watching the game = 298/458 = 0.65
d). Suppose the respondent chosen enjoyed watching the game. What, then, is the probability that the individual is a male?
Suppose the repondent chosen enjoyed watching the game
Probability that the individual is male = No. Men who enjoyed watching the game / No. respondents who ejnoyed the game
From the above table ,
No. Men who enjoyed watching the game =685
No. of respondents who enjoyed the game = 845
Suppose the repondent chosen enjoyed watching the game
Probability that the individual is male = 685/845 = 0.8107
Men Women Total Enjoy 685 160 845 Did not Enjoy 205 298 503 Total 890 458 1348=Grand TotalRelated Questions
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