Free Practice Quiz Question List

9. Confidence Intervals Online Quiz Questions

Use this free practice quiz with 20 questions to review 9. Confidence Intervals, test your knowledge, and prepare for your next test or exam.

20 questions

Choose one

1 point

Which statistic is the point estimate for a population proportion?

A
The sample mean $\bar{x}$
B
The sample proportion $\hat p$
C
The population proportion $p$
D
The margin of error

Choose one

1 point

Which statement correctly interprets the 95% confidence level of a confidence-interval procedure?

A
There is a 95% probability that this particular interval contains the parameter.
B
The sample statistic is correct 95% of the time.
C
About 95% of intervals produced by the method would capture the true parameter.
D
The population parameter changes so that it falls inside 95% of computed intervals.

Choose one

1 point

A random sample is used to estimate a population mean, and the population standard deviation $\sigma$ is unknown. Which procedure is appropriate for a standard introductory confidence interval?

A
Use a t-interval based on $s$ and $n-1$ degrees of freedom.
B
Use a z-interval based on $s$ and $n$ degrees of freedom.
C
Use a proportion interval based on $\hat p$ .
D
Use no interval because the population standard deviation is unknown.

Choose all

1 point

Which conditions support using the normal-approximation confidence interval for one population proportion? Select all that apply.

A
The data come from a random sample or randomized process.
B
The observations are independent, with the 10% guideline when applicable.
C
The sample contains at least 10 observations regardless of the observed proportion.
D
Both the observed success and failure counts are at least 10.

Choose all

1 point

For otherwise comparable confidence intervals, which changes generally increase or decrease the margin of error as described in the material? Select all that apply.

A
Increasing the sample size generally decreases the margin of error.
B
Increasing the sample size generally increases the margin of error.
C
Increasing data variability increases the margin of error.
D
Increasing the confidence level increases the margin of error.

True or false

1 point

True or false: A confidence interval can correct for a biased sampling method if the sample size is sufficiently large.

A
True
B
False

True or false

1 point

True or false: Holding sample size and variability constant, a 99% confidence interval is wider than a 95% confidence interval.

A
True
B
False

Written response

1 point

What is the approximate two-sided standard-normal critical value $z^*$ for a 99% confidence interval? Enter the value rounded to three decimal places.

Written response

1 point

What distribution supplies the critical value for a one-population-mean confidence interval when the population standard deviation is unknown?

Fill in the blank

1 point

A confidence interval combines a point estimate, such as a , with a margin of error to estimate an unknown population .

Fill in the blank

1 point

The margin of error is the product of a and the .

Open ended

1 point

A random sample of 25 packages has mean shipping time $\bar{x}=72.4$ hours and sample standard deviation $s=8.5$ hours. Assume the shipping times are reasonably close to normal and contain no extreme outliers. Using $t^*=2.064$ for 24 degrees of freedom, construct and interpret the 95% confidence interval for the population mean shipping time.

Written response

1 point

In the transportation-app example, what is the approximate margin of error for the 95% confidence interval for the population proportion? Enter the decimal value rounded to three decimal places. An absolute tolerance of 0.001 is accepted.

Choose one

1 point

Which statement correctly interprets a 95% confidence procedure?

A
There is a 95% probability that the fixed population parameter changes into the interval.
B
The sample statistic is within 95% of the population parameter.
C
About 95% of intervals produced by this method in repeated random samples would capture the true parameter.
D
The interval contains 95% of the observations in the population.

Choose one

1 point

If the confidence level and population variability remain fixed, what generally happens to a confidence interval when the sample size increases?

A
The interval generally becomes narrower.
B
The interval generally becomes wider.
C
The center of the interval must move to zero.
D
The confidence level automatically increases.

Choose one

1 point

A random sample has $n=40$ observations and $\hat p=0.20$ . Based on the usual large-count check, should the normal-approximation one-proportion confidence interval be used without further consideration?

A
The condition is met because the sample size is 40.
B
The condition is not met because the observed number of successes is only 8.
C
The condition is met because the observed number of failures is 32.
D
The condition is not met because the sample proportion is greater than 0.50.

Choose one

1 point

A random sample of $n=20$ quantitative observations has unknown population standard deviation, and the sample standard deviation $s$ is used. Which interval procedure is appropriate for the population mean, assuming the other conditions are satisfied?

A
A z-interval with 20 degrees of freedom
B
A z-interval with 19 degrees of freedom
C
A t-interval with 20 degrees of freedom
D
A t-interval with 19 degrees of freedom

Choose one

1 point

A confidence interval for a population mean uses $t^*=2.1$ , sample standard deviation $s=12$ hours, and sample size $n=36$ . What is the margin of error?

A
2.1 hours
B
4.2 hours
C
12.0 hours
D
25.2 hours

Written response

1 point

For a mean confidence interval, suppose $t^*=2.1$ , $s=12$ hours, and $n=36$ . Calculate the margin of error in hours. Enter the result rounded to one decimal place; values within 0.01 hours are accepted.

True or false

1 point

A company will adopt a service only if more than 60% of its customers approve it. A 95% confidence interval for the population approval proportion is 53.2% to 62.8%. True or false: This confidence interval establishes that more than 60% of customers approve the service.

A
True
B
False