Question 1

Which of the following best describes independent sampling?

Accepted Answer

Individuals selected for one sample do not dictate which individuals are in the second sample.

Question 2

A researcher wants to compare the mean weights of 'state' quarters and 'traditional' quarters. He randomly selects 18 'state' quarters and 16 'traditional' quarters. What type of sampling is this?

Accepted Answer

Independent sampling

Question 3

Which formula is used to calculate the test statistic for comparing two population proportions from independent samples?

Accepted Answer

$$z_0$$ = \frac{\hat{p}_1 - \hat{p}_2}{\sqrt{\hat{p}(1-\hat{p})\left(\frac{1}{$$n_1$$} + \frac{1}{$$n_2$$}\right)}}$$

Question 4

In hypothesis testing for two proportions, which condition must be satisfied for the sampling distribution to be approximately normal?

Accepted Answer

$$n_1$$ \hat{p}_1 (1-\hat{p}_1) \geq 10$$ and n_2$ \hat{p}_2 (1-\hat{p}_2) \geq 10$$

Question 5

A 99% confidence interval for the difference between two population proportions is calculated as $$0.4225 - 0.3893 \pm 2.575 \sqrt{0.4225(1-0.4225)/800 + 0.3893(1-0.3893)/750}. $$What does it mean if the interval contains 0?

Accepted Answer

There is insufficient evidence to conclude a difference in proportions.

Question 6

Which test is appropriate for comparing two proportions from dependent samples?

Accepted Answer

McNemar's test

Question 7

Given matched-pairs data, which formula is used to compute the test statistic for the mean difference?

Accepted Answer

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

Question 8

A doctor wants to estimate the difference in proportions of mothers receiving prenatal care between two age groups. She wants the estimate to be within 2 percentage points with 95% confidence and has no prior estimates. What sample size should she use?

Accepted Answer

$$n = 0.5 \left(\frac{1.96}{0.02}\$$right)^2$$

Question 9

Which of the following is a requirement for using the F-test to compare two population standard deviations?

Accepted Answer

The populations must be normally distributed.

Question 10

A researcher tests whether the standard deviation of 'state' quarters is less than that of 'traditional' quarters using the F-test. The test statistic is $$F_0 = 0.52$ and the critical value is F$$_{0.95,17,15} = 0.42$$. What is the correct conclusion?

Accepted Answer

Fail to reject the null hypothesis; there is not enough evidence to conclude the standard deviation is less for 'state' quarters.

Question 11

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

Accepted Answer

$$(x_1$ - x_2$) \pm t_{\alpha/2} \sqrt{\frac{s_1$^2}{n_1$} + \frac{s_2$^2}{n_2$}}$$

Question 12

Which of the following is NOT a characteristic of the F-distribution?

Accepted Answer

It is symmetric.

Question 13

In a right-tailed test for two population proportions, which condition leads to rejection of the null hypothesis?

Accepted Answer

If $$z_0$$ \u003e z_{\alpha}$$

Question 14

Which formula is used to calculate the degrees of freedom for Welch’s t-test?

Accepted Answer

$$df = \frac{\left(\frac{s_1$^2}{n_1$} + \frac{s_2$^2}{n_2$}\$$right)^2$$}{\frac{\left(\frac{s_1$^2}{n_1$}\$$right)^2$$}{n_1$-1} + \frac{\left(\frac{s_2$^2}{n_2$}\$$right)^2$$}{n_2$-1}}$$

Question 15

A matched-pairs t-test is used to compare the mean difference in hotel prices between two chains in 10 cities. The test statistic is $$t_0 = 5.27$ and the critical value is t$$_{0.025} = 2.262$$. What is the correct conclusion?

Accepted Answer

Reject the null hypothesis; there is sufficient evidence the prices differ.

Question 16

Which of the following is a requirement for using the t-test for the difference of two independent means?

Accepted Answer

The samples are obtained using simple random sampling.

Question 17

In a two-tailed test for two population means, which condition leads to rejection of the null hypothesis?

Accepted Answer

If $$t_0  t$$_{\alpha/2}$$

Inference on Two Samples: Proportions, Means, and Standard Deviations

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