A student organization is trying to decide whether or not to offer more movies o
ID: 3074669 • Letter: A
Question
A student organization is trying to decide whether or not to offer more movies on campus. They want to determine whether this idea will appeal to members of both genders. A random sample of 1000 students was asked if they were in favor of more movies on campus. The results by gender are shown in the table below in Figure 2.
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Opinion
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Gender In Favor No Opinion Opposed
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Male 330 165 55
Female 225 180 45
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Fig. 2: Summary
(a) What proportion of the sampled students is in favor of more movies on campus?
(b) What proportion of the sampled females is in favor of more movies on campus?
(c) What proportion of the sampled males is in favor of more movies on campus?
(d) To answer the original question regarding whether or not to offer more movies on campus, which distribution should the student organization study?
i. The joint distribution of gender and opinion.
ii. The marginal distribution of gender.
iii. The conditional distribution of gender given opinion.
iv. The conditional distribution of opinion given gender.
Explanation / Answer
Answer to part a)
Total students in favor = 330+225 = 555
Total students = 1000
Proportion = 555/1000
Proportion = 0.555
.
Answer to part b)
Total females in favor = 225
Total females = 225+180+45 = 450
Proportion = 225/450 = 0.50
.
Answer to part c)
Total males in favor = 330
Total males = 1000-450 = 550
Proportion = 330/550 = 0.60
.
Answer to part d)
The joint distribution is the best because the proportion of females and males in favor is almost same
Hence Joint Distribution of gender and opinion is must
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