Question 1

Which of the following best describes independent samples in the context of hypothesis testing?

Accepted Answer

Samples where the selection of one sample does not affect the selection of the other sample.

Question 2

A researcher wants to compare the mean cholesterol levels of two groups: one group before a diet and the same group after the diet. What type of samples are these?

Accepted Answer

Dependent samples

Question 3

Which of the following is NOT a required condition for performing a two-sample z-test for the difference between means?

Accepted Answer

The samples are dependent.

Question 4

Given two independent samples with known population standard deviations, which formula represents the standard error of the difference between sample means?

Accepted Answer

$$\sqrt{\frac{\$$sigma_1$$^2}{n_1$} + \frac{\$$sigma_2$$^2}{n_2$}}$$

Question 5

What is the null hypothesis ($$H_0) $$when testing the difference between two population means using independent samples?

Accepted Answer

$$\mu_1$ - \mu_2$ = 0$$

Question 6

A credit card watchdog group claims there is a difference in mean credit card debts between two states. Which type of test should be used if the population standard deviations are known and the samples are independent?

Accepted Answer

Two-sample z-test for the difference between means

Question 7

If the calculated z-test statistic falls within the rejection region, what is the appropriate conclusion?

Accepted Answer

Reject the null hypothesis

Question 8

Which of the following scenarios best illustrates the use of a two-sample z-test for the difference between means?

Accepted Answer

Comparing the mean monthly rent in two different cities using independent random samples from each city.

Question 9

Suppose you conduct a two-sample z-test and obtain a p-value of 0.03. If your significance level is $$\alpha = 0.05$$, what should you conclude?

Accepted Answer

Reject the null hypothesis because the p-value is less than $$\alpha.$$

Question 10

Which of the following is a correct interpretation of a two-tailed test in the context of comparing two means?

Accepted Answer

You are testing whether the means are equal or not, regardless of direction.

Question 11

A researcher claims that the average rent in City A is less than in City B. What is the appropriate alternative hypothesis ($$H_a) $$for this left-tailed test?

Accepted Answer

$$\mu_1$ - \mu_2$ \u003c 0$$

Question 12

Which of the following is a reason to use a two-sample z-test instead of a t-test?

Accepted Answer

The population standard deviations are known.

Question 13

In a two-sample z-test, what does it mean if the test statistic $$z is $$not in the rejection region?

Accepted Answer

You fail to reject the null hypothesis.

Question 14

Which of the following best describes the sampling distribution of the difference between two independent sample means when population standard deviations are known?

Accepted Answer

It is a normal distribution with mean $$\mu_1$ - \mu_2$ and standard error $$\sqrt{\frac{\$$sigma_1^2$$}{$$n_1$$} + \frac{\$$sigma_2^2$$}{$$n_2$$}}$$.

Question 15

A psychologist compares the mean scores of two different groups of adults on a screening test. The groups are not paired and have different sample sizes. Which test is appropriate if population standard deviations are known?

Accepted Answer

Two-sample z-test for the difference between means

Hypothesis Testing with Two Samples: Study Notes

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