Question 1

Which of the following best describes the purpose of constructing a confidence interval for a population mean?

Accepted Answer

To estimate the range in which the population mean is likely to fall with a specified level of confidence.

Question 2

A researcher collects a random sample of 106 body temperatures with a mean of 98.20°F and a standard deviation of 0.62°F. What is the correct formula for the margin of error (E) when constructing a confidence interval for the mean using the t-distribution?

Accepted Answer

$$E = t_{\alpha/2} \cdot \frac{s}{\sqrt{n}}$$

Question 3

In Example 1, a 99% confidence interval for the mean body temperature was calculated as (98.04, 98.36). What does this interval mean in practical terms?

Accepted Answer

We are 99% confident that the true mean body temperature of all healthy humans lies between 98.04°F and 98.36°F.

Question 4

When constructing a confidence interval for the mean weight of bumble bats using raw data, which statistical test is most appropriate?

Accepted Answer

TInterval

Question 5

Suppose you have a sample of 15 bumble bat weights. Why is the t-distribution used instead of the normal (z) distribution when constructing the confidence interval?

Accepted Answer

Because the sample size is small and the population standard deviation is unknown.

Question 6

A student calculates a 95% confidence interval for the mean weight of bumble bats as (1.57, 1.86) grams. If the confidence level is increased to 99%, what will happen to the width of the confidence interval?

Accepted Answer

The interval will become wider.

Question 7

Which of the following is NOT a requirement for constructing a confidence interval for a population mean using the t-distribution?

Accepted Answer

The population standard deviation must be known.

Question 8

Given a sample mean $$\bar{x} = 98.20$$, sample standard deviation $$s = 0.62$$, and sample size $$n = 106$$, which formula correctly represents the 99% confidence interval for the population mean $$\mu$$?

Accepted Answer

$$\bar{x} \pm t_{\alpha/2} \cdot \frac{s}{\sqrt{n}}$$

Question 9

A scientist wants to estimate the mean weight of a rare insect species. She collects a random sample of 20 insects and calculates a 95% confidence interval. Which of the following would increase the precision (make the interval narrower) of her estimate?

Accepted Answer

Increasing the sample size.

Question 10

If a sample of 106 body temperatures yields a mean of 98.20°F and a 99% confidence interval of (98.04, 98.36), what is the margin of error?

Accepted Answer

0.16°F

Question 11

A student enters raw data for bumble bat weights into a calculator and selects TInterval. What is the primary reason for using TInterval instead of ZInterval?

Accepted Answer

The population standard deviation is unknown.

Question 12

Which of the following statements about confidence intervals is TRUE?

Accepted Answer

A confidence interval is wider for higher confidence levels.

Question 13

If the sample standard deviation increases while the sample size remains constant, what happens to the width of the confidence interval for the mean?

Accepted Answer

The interval becomes wider.

Question 14

A biologist wants to estimate the mean weight of a population of bats. She collects a sample and calculates a confidence interval. Which of the following would NOT affect the width of the confidence interval?

Accepted Answer

The sample mean.

Question 15

A confidence interval for the mean is calculated as $$\bar{x} \pm t_{\alpha/2} \cdot \frac{s}{\sqrt{n}}. If$$ $$n$$ increases, what happens to $$\frac{s}{\sqrt{n}}$$?

Accepted Answer

It decreases.

Question 16

A medical researcher wants to estimate the mean cholesterol level in a population. She collects a random sample and calculates a confidence interval. Which of the following best explains why the confidence interval might not contain the true mean?

Accepted Answer

The sample is random, but sampling variability means the interval may not always contain the true mean.

Question 17

A student calculates a 95% confidence interval for the mean weight of bumble bats as (1.57, 1.86) grams. If the sample mean is 1.71 grams, what is the correct interpretation?

Accepted Answer

We are 95% confident that the true mean weight of bumble bats is between 1.57 and 1.86 grams.

Question 18

Which of the following would result in a narrower confidence interval for the mean body temperature of healthy humans?

Accepted Answer

Increasing the sample size.

Question 19

A researcher wants to estimate the mean weight of a population of bats. She collects a sample and calculates a confidence interval using the t-distribution. Which of the following is a valid assumption for using the t-distribution?

Accepted Answer

The population is approximately normal or the sample size is large.

Estimating a Population Mean: Confidence Intervals

Study Guide - Practice Questions

Study Guide - Flashcards