Free Practice Quiz Question List

09 Inference for Means and Proportions Online Quiz Questions

Use this free practice quiz with 20 questions to review 09 Inference for Means and Proportions, test your knowledge, and prepare for your next test or exam.

20 questions

Choose one

1 point

When testing $H_0:p=p_0$ with a one-proportion $z$ test, which proportion belongs in the standard-error formula?

A
Use $\hat p$ , because it is the observed estimate.
B
Use $p_0$ , because the standard error is computed under $H_0$ .
C
Use the midpoint between $p_0$ and $\hat p$ .
D
Use the population proportion only if it is known exactly.

Choose one

1 point

Blood pressure is measured for each patient immediately before and after treatment. Which procedure is generally appropriate for comparing the mean change?

A
An independent two-proportion $z$ procedure
B
A pooled two-sample $t$ procedure
C
A paired $t$ procedure on the within-pair differences
D
A one-proportion exact binomial test

Choose one

1 point

A researcher wants a confidence interval for $p_1-p_2$ from two independent binary samples. Which standard-error approach is generally appropriate?

A
An unpooled standard error using both sample proportions separately
B
A pooled standard error based on the common null proportion
C
The standard error for a single population mean
D
No standard error, because proportions are exact

Choose all

1 point

Which two statements correctly describe conditions relevant to inference? Select all that apply.

A
For sampling without replacement, the sample is commonly no more than about 10% of the finite population.
B
A normal approximation for a proportion is valid whenever the sample size exceeds 10.
C
The success-failure check requires both expected successes and expected failures to be sufficiently large.
D
Independence is unnecessary whenever a confidence interval is being constructed.

Choose all

1 point

Which two statements correctly distinguish confidence intervals from hypothesis tests for two independent proportions? Select all that apply.

A
A confidence interval for $p_1-p_2$ generally uses a pooled standard error.
B
A confidence interval for $p_1-p_2$ generally uses an unpooled standard error.
C
A test of $H_0:p_1-p_2=0$ generally estimates each proportion separately for its standard error.
D
A test of $H_0:p_1-p_2=0$ generally uses a pooled standard error.

True or false

1 point

True or false: After a particular 95% confidence interval has been calculated, there is a 95% probability that the fixed population parameter lies inside that interval.

A
True
B
False

True or false

1 point

True or false: In a paired $t$ procedure, the normality condition concerns the distribution of the within-pair differences.

A
True
B
False

Written response

1 point

In a sample of 400 voters, 220 support a proposal. What is the sample proportion $\hat p$ , expressed as a decimal?

Written response

1 point

What is the name of the two-sample $t$ procedure that does not assume equal population variances?

Fill in the blank

1 point

For a hypothesis test of $H_0:p_1-p_2=0$ , the standard error is generally because the null hypothesis assumes a common proportion.

Fill in the blank

1 point

In paired inference, the observations are reduced to within-pair and then analyzed as a one-sample mean problem.

Open ended

1 point

A manufacturer measures the fill volume of 25 randomly selected containers. The sample mean is 503 mL and the sample standard deviation is 8 mL. The population standard deviation is unknown, and the goal is to estimate the population mean fill volume. Which inferential procedure should be used, what is its formula, and what assumptions or conditions should be checked?

Choose one

1 point

Two unrelated groups have quantitative outcomes, and their population variances are not known to be equal. Which procedure is the safest default for comparing their population means?

A
Use Welch's unpooled two-sample procedure.
B
Use the pooled two-sample procedure because all two-sample means require pooling.
C
Use a paired $t$ procedure because there are two groups.
D
Use a one-proportion $z$ procedure because the groups are independent.

Choose one

1 point

A 95% confidence interval for $\mu_1-\mu_2$ is $(2.1,7.4)$ , and the null hypothesis is $H_0:\mu_1-\mu_2=0$ . At the corresponding 5% significance level for a two-sided test, what conclusion is supported?

A
The null value is inside the interval, so reject the null hypothesis.
B
The null value is outside the interval, so reject the null hypothesis.
C
The interval cannot be used to assess the corresponding two-sided test.
D
The null value is outside the interval, so accept the null hypothesis as true.

Choose one

1 point

Blood pressure is measured for each patient immediately before and after treatment. Which procedure is most appropriate for testing whether the treatment changes the population mean blood pressure?

A
An independent two-sample proportion test
B
A paired $t$ procedure on the within-patient differences
C
A one-proportion $z$ test
D
A pooled two-sample $t$ procedure for unrelated groups

Choose one

1 point

A researcher tests $H_0:p=0.40$ using a sample of size $n=250$ . Which proportion belongs in the standard error of the one-proportion hypothesis test?

A
The population proportion estimated by the sample, $\hat p$
B
The sample size divided by the number of successes, $n/X$
C
The null proportion, $p_0$
D
The complement of the sample proportion, $1-\hat p$

True or false

1 point

True or false: After a 95% confidence interval for a population proportion has been calculated, there is a 95% probability that the fixed population proportion lies in that particular interval.

A
True
B
False

Choose one

1 point

A study estimates the difference in renewal proportions between two independent customer groups. Which standard-error choice is generally appropriate for a confidence interval for $p_1-p_2$ ?

A
Use a pooled standard error because the interval concerns two groups
B
Use an unpooled standard error based on both separate sample proportions
C
Use the null proportion $p_0$ in both groups
D
Use a pooled variance from a two-sample $t$ procedure

Written response

1 point

What is the name of the unpooled two-sample procedure for comparing two independent population means when equal population variances are not assumed?

Written response

1 point

A manufacturer claims that the mean fill volume is $500$ mL. A sample has $n=25$ , $\bar{x}=503$ mL, and $s=8$ mL. For the test $H_0:\mu=500$ , calculate the test statistic $t$ .