Question 1

Which of the following best describes a dependent (matched-pairs) sample?

Accepted Answer

A sample where each individual in one group is paired with an individual in another group based on a shared characteristic.

Question 2

A researcher wants to compare the proportion of smokers in two cities. Which formula should be used to compute the test statistic for the difference in proportions?

Accepted Answer

$$Z = \frac{\hat{p}_1 - \hat{p}_2}{\sqrt{\hat{p}(1-\hat{p})(1/n_1$ + 1/n_2$)}}$$ where $$\hat{p} is $$the pooled proportion

Question 3

In a study comparing the mean wait times at two amusement park rides using matched-pairs data, which test statistic is appropriate?

Accepted Answer

$$t_0$$ = \frac{\bar{d} - \mu_d}{s_d/\sqrt{n}}$$

Question 4

Which condition must be met to use the F-test for comparing two population variances?

Accepted Answer

The populations must be normally distributed.

Question 5

A doctor wants to estimate the difference in proportions of prenatal care between two age groups. If no prior estimates are available, what sample size formula should she use?

Accepted Answer

$$n = \frac{z_{\alpha/2}^2 \cdot 0.5 \cdot 0.5}{E^2$}$$

Question 6

When constructing a confidence interval for the difference between two independent means, which formula is used?

Accepted Answer

$$(\bar{x}_1 - \bar{x}_2) \pm t_{\alpha/2} \sqrt{\frac{s_1$^2}{n_1$} + \frac{s_2$^2}{n_2$}}$$

Question 7

In hypothesis testing for two population proportions, which requirement ensures the sampling distribution is approximately normal?

Accepted Answer

Each sample size must satisfy $$n_1$$ \hat{p}_1 \geq 10$$ and n_2$ \hat{p}_2 \geq 10.$$

Question 8

A student wants to test if the mean wage differs between male and female college students using independent samples. Which test statistic should be used?

Accepted Answer

$$t_0$$ = \frac{(\bar{x}_1 - \bar{x}_2) - (\$$mu_1$$ - \$$mu_2$$)}{\sqrt{\frac{$$s_1^2$$}{$$n_1$$} + \frac{$$s_2^2$$}{$$n_2$$}}}$$

Question 9

Which of the following is NOT a requirement for using the F-test to compare two population standard deviations?

Accepted Answer

The sample sizes must be equal.

Question 10

In a right-tailed test for the difference of two means using independent samples, what is the decision rule for the classical approach?

Accepted Answer

Reject the null hypothesis if $$t_0$$ \u003e t_{\alpha}$$.

Question 11

A survey finds that 37% of Democrats and 55% of Republicans believe the economic system is fair. Which statistical test should be used to compare these proportions?

Accepted Answer

A test for the difference between two independent proportions.

Question 12

Which of the following best describes the shape of the F-distribution?

Accepted Answer

Skewed right, with values always greater than or equal to zero.

Question 13

When testing hypotheses about the mean difference in matched-pairs data, which degrees of freedom are used?

Accepted Answer

$$n - 1$$, where $$n is $$the number of pairs.

Question 14

A confidence interval for the difference in proportions between two groups is constructed. Which interpretation is correct?

Accepted Answer

The interval estimates the difference in proportions between the two populations with a specified level of confidence.

Question 15

Which scenario requires the use of a matched-pairs t-test?

Accepted Answer

Comparing the mean IQ of siblings, one raised by biological parents and one by adoptive parents.

Question 16

If the P-value in a hypothesis test is less than the significance level $$\alpha$$, what should you conclude?

Accepted Answer

Reject the null hypothesis.

Question 17

Which formula is used to compute the test statistic for comparing two population standard deviations?

Accepted Answer

$$F = \frac{s_1$^2}{s_2$^2}$$

Chapter 11: Inference on Two Population Parameters: Hypothesis Testing and Confidence Intervals

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