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AP Statistics 6.2 Constructing a Confidence Interval for a Population Proportion - MCQs - Exam Style Questions

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Question

A scam call is a call made to deceive the person receiving the call. A report claims that \(45\%\) of all calls received on mobile phones can be classified as scam calls. A mobile phone service believes that the percent of scam calls is different than \(45\%\). Let \(p\) represent the population proportion of mobile phone calls that can be classified as scam calls.
A random sample of calls received on mobile phone devices was selected in order to construct a \(95\%\) confidence interval for estimating \(p\).
Assuming the conditions of inference were met, at a \(0.05\) level of significance, which of the following would provide evidence to reject the report’s claim?
(A) The interval contains \(0.45\).
(B) The interval does not contain \(0.45\).
(C) The interval contains \(0\).
(D) The interval does not contain \(0\).
(E) The interval contains the sample proportion.
▶️ Answer/Explanation
Detailed solution
The report’s claim is \(p=0.45\). At the \(0.05\) level, evidence against the claim occurs if a \(95\%\) confidence interval for \(p\) excludes \(0.45\).
• If the interval contains \(0.45\), the claim is plausible ⇒ do not reject. (A) ✗
• If the interval does not contain \(0.45\), the claim is not plausible ⇒ reject. (B) ✓
• Options (C) and (D) are irrelevant; \(0\) is not the hypothesized value. ✗
• (E) True but always the case for a standard CI and does not address the claim. ✗
✅ Answer: (B)

Question

The back-to-back stemplot shows the list prices for a random sample of 26 new math textbooks and another random sample of 26 new science textbooks at a major university.
List Prices Based on Type of Book
Math Textbook PricesStemScience Textbook Prices
4 3 203 3 4
9 905 5 5 7 7 7 8 9
3 3 3 3 3 3 3 3 1 1 010 3 3 4 4
7 7 7 5 5 5 5 515 7 7 8 9 9 9
8 420 0 4
Key: 1 | 3 represents $130
Based on the back-to-back stemplot, which of the following statements about the textbook prices must be true?
(A) Both math and science textbooks have the same minimum price.
(B) Both math and science textbooks have the same maximum price.
(C) The median of the price of math textbooks is less than that of science textbooks.
(D) The interquartile range of the price of math textbooks is less than that of science textbooks.
(E) The range of the price of math textbooks is less than that of science textbooks.
▶️ Answer/Explanation
Why (D) must be true

From the corrected stemplot, the middle 50% of math prices (between \(Q_1\) and \(Q_3\)) occupies a shorter run of stems/leaves than the middle 50% for science, so the IQR for math is smaller.
The plot does not force the minimums, maximums, or medians to be equal or ordered without additional marking; only the relative central spread is clear.
✅ Answer: (D) The IQR of math prices is less than that of science prices.

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