Free Practice Quiz Question List

07 Confidence Intervals Online Quiz Questions

Use this free practice quiz with 20 questions to review 07 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 of a population proportion $p$ ?

A
The sample size $n$
B
The sample proportion $\hat{p}=x/n$
C
The population proportion $p$
D
The margin of error

Choose all

1 point

Select all changes that generally reduce the margin of error of a confidence interval, assuming the other relevant conditions are held constant.

A
Increase the sample size.
B
Decrease population variability.
C
Increase the confidence level while keeping all else unchanged.
D
Use a lower confidence level.

True or false

1 point

True or false: A 95% confidence procedure means that approximately 95% of intervals produced by the same method in repeated sampling would contain the true population parameter.

A
True
B
False

Written response

1 point

A confidence interval for a population mean uses a $t$ critical value with a sample size of $n=18$ . What degrees of freedom should be used?

Fill in the blank

1 point

Complete the statement: When the population standard deviation is unknown, a confidence interval for a population mean uses a critical value from the with degrees of freedom.

True or false

1 point

True or false: When a sample-size calculation produces a noninteger result, rounding down is acceptable because the difference is usually small.

A
True
B
False

Choose one

1 point

A researcher plans to construct a normal-approximation confidence interval for a population proportion. Which condition should be checked first?

A
Use the normal approximation automatically whenever the sample proportion is close to 0 or 1.
B
Check that the expected numbers of successes and failures are both adequately large.
C
Use a $t$ critical value because the proportion is estimated from a sample.
D
Use the normal approximation only when the population standard deviation is known.

Fill in the blank

1 point

Complete the definition: The margin of error is the .

Choose all

1 point

Select all conditions that should be checked before interpreting a confidence interval.

A
The sample should reasonably represent the target population.
B
Observations should be independent, or the design should account for dependence.
C
The confidence level alone guarantees validity, regardless of the sampling method.
D
The normal or $t$ -based method should be appropriate for the sample size and population shape.

Open ended

1 point

Explain what a 95% confidence level means and why it is not accurate to say that a particular completed interval has a 95% probability of containing the fixed population parameter.

Choose one

1 point

When planning a sample size for a population proportion with no prior estimate of $p$ , why is $p^*=0.50$ used?

A
It minimizes the confidence level.
B
It makes the margin of error equal to zero.
C
It gives the largest value of $p^*(1-p^*)$ and therefore the largest conservative sample size.
D
It is required only when the population standard deviation is known.

Choose one

1 point

A survey estimates the proportion $p$ of residents who support a proposal. Which statistic is the point estimate of $p$ ?

A
The sample mean $\bar{x}$
B
The sample proportion $\hat{p}$
C
The sample standard deviation $s$
D
The population proportion $p$

Choose one

1 point

Which statement correctly interprets a 95% confidence procedure for a population mean?

A
There is a 95% probability that this completed interval contains the parameter.
B
The sample statistic is correct 95% of the time.
C
Approximately 95% of intervals produced by the procedure would contain the true parameter.
D
The parameter has a 95% chance of changing during repeated sampling.

Choose one

1 point

A population standard deviation is known to be $\sigma=12$ . For a sample of size $n=100$ , what is the 95% margin of error for estimating the population mean? Use $z^*=1.96$ .

A
$1.96\left(\frac{12}{\sqrt{100}}\right)=2.352$
B
$1.96\left(\frac{12}{100}\right)=0.2352$
C
$1.96\left(\frac{100}{\sqrt{12}}\right)=56.58$
D
$1.96(12)(100)=2352$

Choose one

1 point

A random sample has $n=16$ , sample mean $\bar{x}=42$ , and sample standard deviation $s=6$ . The population standard deviation is unknown. Which method and degrees of freedom should be used for a two-sided confidence interval for the population mean?

A
Use $z^*$ with $df=16$ because the sample has 16 observations.
B
Use $z^*$ with $df=15$ because the sample standard deviation is available.
C
Use $t^*$ with $df=16$ because the sample has 16 observations.
D
Use $t^*$ with $df=15$ because $df=n-1$ .

Choose one

1 point

A mean is to be estimated with 95% confidence, maximum margin of error $E=3$ , and planning value $\sigma=12$ . Using $z^*=1.96$ , the calculation gives $n=61.47$ . What minimum integer sample size is required?

A
60
B
62
C
61
D
63

True or false

1 point

True or false: A confidence interval for a population mean is intended to estimate the range in which individual observations will fall.

A
True
B
False

Written response

1 point

A population standard deviation is known to be $\sigma=10$ . A sample has $n=100$ and $\bar{x}=50$ . Using $z^*=1.96$ , what is the upper endpoint of the 95% confidence interval for the population mean?

Written response

1 point

What statistical term describes the distance from the point estimate to either endpoint of a symmetric confidence interval?

Written response

1 point

A researcher plans a confidence interval for a population mean using $z^*=1.96$ , a planning value of $\sigma=15$ , and a maximum acceptable margin of error of $E=3.5$ . Before any upward rounding to a whole number, what sample size does the planning formula produce?