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AP Statistics 8.4 Expected Counts in Two-Way Tables - MCQs - Exam Style Questions

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Question

A research group conducted a study to investigate whether there is an association between age-group and electronic device preference for sending e-mails. A random sample of 216 adults was selected. The table shows the results of the study.
Preferred Way to Send E-mails by Age-Group
 19 to 38 years39 to 58 years59 to 78 yearsTotal
Cell phone47241889
Laptop2230759
Tablet12342268
Total818847216
Assume the conditions for inference have been met. If a chi-square test of independence is conducted, which of the following will be closest to the expected number of adults ages 39 to 58 years who prefer using a tablet for sending e-mails?
(A) 1.4
(B) 23.7
(C) 27.7
(D) 29.3
(E) 34
▶️ Answer/Explanation
Detailed solution
Expected count formula for a cell: \(E=\dfrac{(\text{row total})(\text{column total})}{\text{grand total}}\).
Here (Tablet row total) \(=68\), (39–58 column total) \(=88\), grand total \(=216\).
\(E=\dfrac{68\times 88}{216}=\dfrac{5984}{216}\approx 27.7\).
✅ Answer: (C) 27.7

Question

First-year students enrolled at a college were asked whether they play video games. The responses, classified by whether the students were enrolled in the school of sciences or the school of arts, are shown in the table.
 Play Video GamesDo Not Play Video GamesTotal
Sciences519120639
Arts347446793
Total8665661,432
Of all the students enrolled in the school of arts who responded, approximately what proportion responded that they play video games?
(A) 0.242
(B) 0.401
(C) 0.438
(D) 0.554
(E) 0.605
▶️ Answer/Explanation
Detailed solution

1. Identify the Relevant Numbers:
– The number of students in Arts who play video games is 347.
– The total number of students in Arts is 793.

2. Calculate the Proportion:
The proportion is the number of interest divided by the total for that group.
Proportion = $\frac{\text{Arts students who play video games}}{\text{Total Arts students}}$

3. Solve:
Proportion = $\frac{347}{793} \approx 0.43757…$

This value rounds to 0.438.
✅ Answer: (C)

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