Question

Use the following information to answer the next 4 questions./ Several semesters ago, a group of students took an SRS from the class roster, and asked each subject two questions: whether or not they own a maroon car and whether or not they come from an Aggie family. The results are given below. They wanted to use their data to test their hypothesis that a higher proportion of students from an Aggie family had maroon cars than students not from an Aggie family Family By Car Color Count Row % Expected From Aggie family Has Maroon Doesn't otal havecount maroon car 29 80.56 32.4 79 94.05 75.6 108 36 Test Likelihood Ratio Pearson ChiSquare Prob ChiSq 0.0312 0.0240 19.44 3.6 5 5.95 8.4 12 4.642 5.097 Not from Aggie family 84 20 17. What hypotheses would you use to test your claim? a) Ho : PA = PNA versus H.-Pa > PNA where PA = proportion of students coming from an Aggie family whose car color is maroon and pNA proportion of students who do not come from an Aggie family whose car color is maroon. b) Ho PA PNA versus H. Pa PNA where pproportion of students coming from an Aggie family whose car color is maroon and PNA proportion of students who do not come from an Aggie family whose car color is maroon. e Ho PMP versus Ha PM PNM where pM proportion of students whose car color is maroon that come from a Aggie family and pNM proportion of students whose car color is not maroon that come from a Aggie family d) H) : рм-wil versus Ha : Pa, PNM where pal proportion of students coming from an Aggie family whose car color is maroon and pNMproportion of students coming from an Aggie family whose car color is not maroon. e) Exactly two of the above are correct. 18. What p-value shonld the researchers use? a) 0.0240 b) 0.0309 c) 0.0312 d) 0.0416 e) The conditions arent met by the chi-squared test so the p-value is not valid 19 Compute the relative risk of having a maroon car between students coming from an Aggie family compared to students who dont come from an Aggie family. a) 0134 b) 086 1.17 d) 3.27 e) 418 20. Suppose the relative risk above were 2.8 (this is not coect). Interpret what this means in the context of the situation a) Students from an Aggie family are 2.8 times as likely to own a maroon car as thoee who do not come from an Aggie family car as those who come from an Aggie family who do not come from an Aggie family than those who come from an Aggie family those who come from an Aggie family b) Students who do not come from an Aggie family are 2.8 times as likely to own a maroon e) Students from an Aggie family are 2.8 times less likely to own a maroon car than thoee d) Students who come from an Aggie family are 28% more likely to own a maroon car e) Students who come from an Aggie family are 28% as likely to own a maroon car as End group of related questions.j

Answer 1

17.

Answer: Option A

Hypothesis that would be used to test the claim

1. H_{0}:p_{A} = p_{NA} versus H_{a}:p_{A} > p_{NA}

18.

Answer: Option A

0.0240 is the p-value that researchers should use

19.

Answer: Option D

Relative Risk = (7/36)/(5/84) = 3.27

20.

Answer: Option A

Students from an Aggie family are 2.8 times as likely to own a maroon car as those who do not come from an Aggie family