AnswersCA-Statistics and Probability BEstimating a Population Proportion

Estimating a Population Proportion Answers

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1
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A producer of 10-ounce bags of pretzels claims that less than 7% of the pretzels in each bag are broken. The 95% confidence interval for the true proportion of broken pretzels in the 10-ounce bags produced by this company is (0.036, 0.067). Is it reasonable to conclude that less than 7% of pretzels in each bag are broken?

A
Yes, because the entire interval is less than 0.07.
B
Yes, because the center of the interval is 0.0515, which is less than 7%.
C
No, because a different sample might give different results.
D
No, because the interval has many values that are plausible.
2
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A guidance counselor is studying test anxiety in freshman students. A random sample of 972 high school freshmen finds that 219 of these students have had some form of test anxiety. A 95% confidence interval for the proportion of freshmen with test anxiety is (0.199, 0.252). Which statement correctly interprets the interval?

A
The guidance counselor can be 95% confident that 23% of freshmen will have some form of test anxiety.
B
There is a 95% probability that the proportion of freshmen with test anxiety lies between 0.199 and 0.252.
C
If this procedure is repeated many, many times, the true proportion of freshmen with test anxiety will be captured 95% of the time.
D
The guidance counselor can be 95% confident that the interval from 0.199 to 0.252 captures the true proportion of all freshmen who have test anxiety.
3

Ann selects a sample of 29 students at her large high school and finds that 12 of them are planning to travel outside of the state during the coming summer. She wants to construct a confidence interval for p = the proportion of all students at her school who plan on traveling outside of the state during the coming summer, but she realizes she hasn’t met all the conditions for constructing the interval. Which condition for this procedure has she failed to meet?

A
n p hat greater-than-or-equal-to 10
Option A
B
n (1 minus p hat) greater-than-or-equal-to 10
Option B
C
The sample must be a random sample from the population.
D
The sample size must be less than 10% of the population size.
4

A random sample of adults was surveyed about their exercise habits. Of the 100 surveyed, 56 stated they exercise regularly. Which of the following is the 95% confidence interval for p, the proportion of all adults who exercise regularly?Find the z-table here.

A
(0.50, 0.62)
B
(0.48, 0.64)
C
(0.46, 0.66)
D
(0.43, 0.69)
5

According to a recent random survey of 1,963 high school students, 581 report playing a musical instrument. A 90% confidence interval for the population of high school students who play a musical instrument is constructed. Which statement identifies what is being estimated?Find the z-table here.

A
The proportion being estimated is .
Option A
B
The true proportion of high school students who play a musical instrument is p.
C
The true proportion of high school students who play a musical instrument is .
Option C
D
The sample proportion of high school students who play a musical instrument is .
Option D
6

A politician estimates that 61% of his constituents will vote for him in the coming election. How many constituents are required for a random sample to obtain a margin of error of at most 0.03 with 95% confidence?Find the z-table here.

A
716
B
1,016
C
1,068
D
1,755
7

A technology company claims that 13% of customers who call the help desk cannot log in because they have their keyboard on caps lock, which blocks the log in process due to password case sensitivity. Brian, a help desk worker at this company, thinks this proportion is higher. The 95% confidence interval for the true proportion of customers who cannot log in due to caps lock is (0.128, 0.185). Is it reasonable to believe the true proportion of customers who cannot log in due to caps lock is greater than 13%?

A
Yes, because most of the values in the interval are above 0.13.
B
Yes, because the center of the interval is 0.1565, which is greater than 0.13.
C
No, because 0.13 is in the interval.
D
No, because there are values in the interval that are less than 0.13.
8

At a 95% confidence interval for p, the proportion of all US adults who exercise regularly is 0.562 to 0.684. Is it reasonable to believe more than two-thirds of US adults exercise regularly?

A
Yes, because 0.667 is in the interval.
B
Yes, because there are values greater than 0.667 in the interval.
C
No, because there are values less than 0.667 in the interval.
D
No, because the center of the interval is 0.623, which is less than 0.667.
9

A school principal claims the graduation rate at a school is 96%. Molly, a student at this school, takes a random sample of students and finds the 95% confidence interval for the true proportion of students graduating from this school is (0.934, 0.983). Is it reasonable to conclude the principal’s claim is incorrect?

A
No, because the interval contains 0.96.
B
No, because the interval contains values greater than 0.96.
C
Yes, because the interval has values less than 0.96.
D
Yes, because a different sample might give different results.
10

A researcher takes a random sample of 2,496 drivers and finds that 1,603 put their phone in "drive mode” to not be distracted while driving. A 90% confidence interval for the proportion of drivers who use "drive mode” on their phones is (0.626, 0.658). Which statement correctly interprets the interval?

A
The researcher can be 90% confident that 64% of all drivers will use “drive mode” while driving.
B
There is a 90% probability that the proportion of drivers who use “drive mode” lies between 0.626 and 0.658.
C
The researcher can be 90% confident that the interval from 0.626 to 0.658 captures the true proportion of all drivers who use “drive mode.”
D
If this procedure is repeated many, many times, the true proportion of drivers who use “drive mode” will be captured 90% of the time.

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