Question

5. How heavy are the backpacks carried by college students? To estimate the weight of

backpacks carried by college students, a researcher weighs the backpacks from a random

sample of 58 college students. The average backpack weight ends up being 15.7 pounds,

with a standard deviation of 2.4 pounds. If you use this data to construct a 90% confidence

interval, what will the margin of error be for this interval? Try not to do a lot of

intermediate rounding until you get to the end of your calculations, and choose the answer

below that is closest to what you obtain.

A. 1.65 pounds

B. 3.39 pounds

C. 0.52 pounds

D. 0.07 pounds

E. 0.22 pounds

6. A 95% confidence interval is constructed in order to estimate the average test score for a

population of engineering students. The interval ends up between from 75.42 to 86.58.

Which of the following could be a 99% confidence interval for the same data?

I. 80.21 to 81.79

II. 73.67 to 88.33

III. 78.71 to 83.29

A. I only

B. II only

C. III only

D. I and II

E. II and III

7. An educator is interested in the study habits of students at Degrassi Junior High School. She

is able to survey a random sample of 128 students about their study habits. It is observed

that the average amount of time these students spend working on homework per night is 38

minutes, with a standard deviation of 4.8 minutes. When a 95% confidence interval is

constructed, the interval ends up being from 37.17 minutes to 38.83 minutes. To interpret

this interval, the educator says “We are 95% confident that the mean amount of time all

students at Degrassi Junior High School spend on homework per night is between 37.17

minutes and 38.83 minutes.” What is wrong with this interpretation?

A. Nothing is wrong.

B. The educator must have made a mistake in her calculations because the numbers

37.17 and 38.83 are not correct.

C. The educator should have constructed a 99% confidence interval rather than a 95%

confidence interval.

D. The educator should be stating that she is 95% confident the mean of the sample of

128 students, not the population mean, will be within the computed interval.

E. The educator should be using a sample size of at least 200 students if her goal is to

construct a confidence interval.

8. What proportion of college students listen to podcasts? To estimate this, Jill gathers data

from a random sample of college students and constructs a 95% confidence interval. The

interval is from 0.44 to 0.62. From this information, we can conclude the margin of error is

A. 0.05.

B. 0.09.

C. 0.18.

D. 1.96.

E. It’s impossible to answer this question without more information.

9. Which one of the following statements is false?

A. Confidence intervals are constructed with the goal of estimating an unknown

population parameter.

B. When constructing a confidence interval, the value added to and subtracted from the

sample statistic is called the margin of error.

C. The width of a confidence interval is affected by the size of the sample.

D. If you construct a confidence interval for a population proportion and the interval

ends up being from 0.13 to 0.24, this means the population proportion is definitely

between 0.13 and 0.24.

E. Given the same sample of data, a 99% confidence interval will be wider than a 90%

confidence interval.

10. Which one of the following statements is true?

A. If you construct a confidence interval to estimate a population mean, the margin of error

will get larger as the size of the sample mean increases.

B. The margin of error is affected by the size of the population.

C. The sample statistic (either a mean or a proportion) used to construct the confidence

interval will always be right in the center of the confidence interval.

D. The margin of error takes into account all possible things (e.g., both sampling and

nonsampling errors) that can go wrong when sampling from a population.

E. If you construct a confidence interval to estimate a population mean, the margin of error

will get smaller as the sample standard deviation gets larger.

Answer 1

6. Option II. 73.67 to 88.33 i.e. B. II only

Note: length of 99% CI is larger than length of 95% CI.

7.

One-Sample T

N Mean StDev SE Mean 95% CI
128 38.000 4.800 0.424 (37.160, 38.840)

Option  A. Nothing is wrong.

8.

Margin of error=(0.62-0.44)/2=0.09

Option: B. 0.09.

9. Option: D. If you construct a confidence interval for a population proportion and the interval

ends up being from 0.13 to 0.24, this means the population proportion is definitely

between 0.13 and 0.24.

10. Option: C. The sample statistic (either a mean or a proportion) used to construct the confidence

interval will always be right in the center of the confidence interval.