Question 1

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

Accepted Answer

Samples where there is no relationship between the two samples and they are mutually exclusive.

Question 2

A researcher measures the cholesterol levels of 50 patients before and after a new diet. What type of samples are these?

Accepted Answer

Dependent samples

Question 3

Which formula gives the standard error of the difference between two independent means when population variances are known?

Accepted Answer

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

Question 4

When should you use a two-sample t-test instead of a two-sample z-test?

Accepted Answer

When the population means are unknown and the sample sizes are small.

Question 5

Given the following data from a credit card debt study: $$\bar{x}_1 = 5271$$, $$n_1 = 250$ (Oklahoma), $$\bar{x}_2 = 5121$$, n_2$ = 250 ($$North Carolina), $$\$$sigma_1$$ = 960$$, $$\$$sigma_2$$ = 845. $$What is the value of the test statistic for a two-sample z-test?

Accepted Answer

$$ z = \frac{5271 - 5121}{\sqrt{\frac{960^2$}{250} + \frac{845^2$}{250}}} $$

Question 6

What is the correct degrees of freedom for a two-sample t-test with independent samples and equal variances, where $$n_1 = 15$ and n_2$ = 20$$?

Accepted Answer

$$ d.f. = n_1$ + n_2$ - 2 = 33 $$

Question 7

A study compares the effectiveness of two teaching methods on test scores. Method 1: $$n_1 = 10$, s_1$^2 = 70.661$$; Method 2: $$n_2 = 10$, s_2$^2 = 85.378. $$What is the pooled variance estimate?

Accepted Answer

$$ s_p^2$ = \frac{(n_1$-1)s_1$^2 + (n_2$-1)s_2$^2}{n_1$ + n_2$ - 2} = 78.0222 $$

Question 8

Which of the following scenarios requires a dependent samples t-test?

Accepted Answer

Comparing blood pressure before and after treatment in the same group of patients.

Question 9

What is the formula for the test statistic in a paired (dependent) samples t-test?

Accepted Answer

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

Question 10

Why is it inappropriate to use the independent samples t-test formula for dependent samples?

Accepted Answer

It overestimates the standard error because it ignores the overlap (covariance) between paired scores.

Question 11

Which of the following is NOT an assumption for the two-sample z-test for the difference between means?

Accepted Answer

The population means are unknown.

Question 12

In the context of hypothesis testing, what does the rejection region represent?

Accepted Answer

The range of values for which the null hypothesis is rejected.

Question 13

If the calculated z-value is 1.85 and the critical value for a two-tailed test at $$\alpha = 0.05 is$$ $$\pm 1.96$$, what is the correct conclusion?

Accepted Answer

Fail to reject the null hypothesis.

Question 14

Which of the following best explains why the t-distribution is used instead of the z-distribution for small samples?

Accepted Answer

The t-distribution accounts for the extra uncertainty in estimating the population standard deviation from a small sample.

Question 15

A researcher wants to test if a new training method improves running speed. The average speed for men is 10.5 m/s and for women is 9.5 m/s. If the sample mean difference is greater than 1.0 m/s, what does this indicate?

Accepted Answer

The new method has an effect over and above the known gender difference.

Chapter 8- Hypothesis Testing with Two Samples: Independent and Dependent Samples, z-Tests, and t-Tests

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