AnswersCA-Statistics and Probability BIntroduction to Confidence Intervals

Introduction to Confidence Intervals Answers

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Twenty-four pairs of adult brothers and sisters were sampled at random from a population. The difference in heights, recorded in inches (brother’s height minus sister’s height), was calculated for each pair. The 95% confidence interval for the mean difference in heights for all brother-and-sister pairs in this population was (–0.76, 4.34). What was the sample mean difference from these 24 pairs of siblings?

A
–0.76 inches
B
0 inches
C
1.79 inches
D
4.34 inches
2
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A clinic measured the systolic blood pressure for a random sample of 10 patients. The resulting 95% confidence interval for the mean systolic blood pressure of all the patients at this clinic was (111.3, 129.5). What was the mean systolic blood pressure from the sample of 10 patients?

A
18.2
B
111.3
C
120.4
D
129.5
3

A newspaper poll found that 54% of the respondents in a random sample of voters in the city plan to vote for candidate Roberts. A 95 percent confidence interval for the population proportion is 0.54 ± 0.06. What is the correct interpretation of the 95% confidence interval?

A
We are 95% confident that 54% of all voters would vote for Roberts.
B
There is a 5% chance that less than 48% or more than 60% of voters would vote for Roberts.
C
There is a 95% probability that Roberts would receive between 48% and 60% of the votes.
D
We are 95% confident that the interval from 0.48 to 0.60 captures the true proportion of voters who would vote for Roberts.
4

A random sample of Roosevelt High School students was asked if they prefer taking notes on a computer or using a paper and pencil. Of the 180 students who were surveyed, 75 said they preferred using the computer. The resulting 99 percent confidence interval for the proportion of students who prefer taking notes on the computer was (0.322, 0.511). The school newspaper ran a story saying that less than half of the student body prefers taking notes on a computer. Based on the interval, is the newspaper justified in its statement?

A
Yes. The sample proportion of students who prefer taking notes on their computer was 0.417, which is less than 0.5.
B
Yes. Since nearly the entire confidence interval contains values less than 0.5, we can be certain that less than 50% of students prefer using a computer for notes.
C
No. Since the interval contains values above 0.5, it is plausible that more than 50% of students prefer using a computer for notes.
D
No. Since the interval contains values above 0.5, we can be certain that more than 50% of students prefer using a computer for notes.
5

A credit card company is interested in the proportion of its customers who pay their minimum balance on time. The company randomly sampled 500 records from the previous month. The 95% confidence interval for the true proportion of customers who pay on time was (0.765, 0.835). What are the point estimate and the margin of error for this interval?

A
The point estimate is 0.765, the margin of error is 0.835.
B
The point estimate is 0.765, the margin of error is 0.07.
C
The point estimate is 0.80, the margin of error is 0.035.
D
The point estimate is 0.80, the margin of error is 0.07.
6

An inspector inspects large truckloads of potatoes to determine the proportion with blemishes prior to using the potatoes to make potato chips. She intends to compute a 95% confidence interval for this proportion. To do so, she selects a simple random sample of 90 potatoes, and finds 12 with blemishes. The 95% confidence interval is (0.063, 0.204). What is the correct interpretation for this confidence interval?

A
The inspector can be 95% confident that the proportion of potatoes with blemishes is 0.133.
B
In 95% of samples taken, between 6.3% and 20.4% of the sampled potatoes would have blemishes.
C
The inspector can be 95% confident that the interval from 0.063 to 0.204 captures the proportion of all potatoes on the truck with blemishes.
D
There is a 5% probability that the proportion of all potatoes that have blemishes is either below 0.063 or above 0.204.
7

A researcher for a polling organization used a random sample of 1,540 residents in a city to construct a 95 percent confidence interval for the proportion of voters who would vote for candidate Jones. The resulting confidence interval was 0.480 ± 0.025. What is the correct interpretation of the confidence interval?

A
A proportion of 0.455 and 0.505 of respondents think that Jones has a 95% chance to win.
B
If 95% of all the voters voted, then Jones would receive between 45.5% and 50.5% of the votes.
C
The polling organization can be 95% confident that the interval from 0.455 to 0.505 captures the proportion of all city voters who would vote for Jones.
D
If we repeatedly sampled voters from this city, taking samples of size 1,540, approximately 95% of those samples would have between 45.5% and 50.5% voting for Jones.
8

A study was done to estimate the mean commute time for a population of employed adults. A random sample of 25 employed adults in a particular city was taken, and the 95% confidence interval for mean commute time was calculated to be 34.42 ± 8.14 minutes. A councilman is advocating for road repairs and states that, in this city, people with jobs commute an average of 45 minutes to work each day. Does the confidence interval justify the councilman’s statement?

A
No, because 45 minutes is greater than the upper bound of the confidence interval.
B
Yes, because 45 minutes is greater than the upper bound of the confidence interval.
C
No, because the mean commute time from the 25 sampled adults was 34.42 minutes.
D
Yes, because there were almost certainly some people in the sample of 25 adults whose commute was greater than 45 minutes.
9

A yogurt company claims that it prints a free yogurt coupon under a randomly selected 20% of its lids. A loyal customer purchases 85 yogurt cups, and records whether each was a winner. After consuming all 85 cups, he is disappointed to see that only 12 (14.1%) of his yogurt cups contained coupon codes. He performs a 99% confidence interval for the proportion of yogurt cups containing coupon codes, obtaining (0.044, 0.238). What conclusion can the customer draw about the yogurt company’s claim?

A
The company’s claim may be justified because 0.2 is in the confidence interval.
B
The company’s claim is definitely justified because 0.2 is in the confidence interval.
C
The company’s claim is not justified because the upper endpoint of the confidence interval is 0.238.
D
The company’s claim is not justified because 12 out of 85 (0.141) is far less than 0.2.
10

A newspaper poll found that 54% of the respondents in a random sample of voters in the city plan to vote for candidate Roberts. A 95 percent confidence interval for the population proportion is 0.54 ± 0.06. Based on this interval, what can the newspaper report?

A
There is a 95% chance that Roberts will win.
B
The race is too close to call, so no prediction about who will win should be made.
C
With 95% confidence, there is convincing evidence that Roberts will win.
D
The poll predicts Roberts will win, but there is a 5% chance that the prediction is incorrect due to sampling error.

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