Question 1

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

Accepted Answer

Samples where there is no relationship between the two groups and each participant is in only one group.

Question 2

A researcher measures triglyceride levels in 70 patients before and after a drug treatment. What type of samples are these?

Accepted Answer

Dependent samples

Question 3

Which formula gives the standard error for 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 sample sizes are less than 30 and population variances are unknown

Question 5

A study compares the mean credit card debt of 250 people in Oklahoma ($$\bar{x}_1 = 5271) $$and 250 people in North Carolina ($$\bar{x}_2 = 5121$$), with $$\$$sigma_1$$ = 960$$ and $$\$$sigma_2$$ = 845. $$What is the null hypothesis for this two-sample z-test?

Accepted Answer

$$ H_0$: \mu_1$ = \mu_2$ $$

Question 6

Which of the following is a key assumption for using the two-sample z-test for the difference between means?

Accepted Answer

The population standard deviations are known

Question 7

Why is the pooled variance used in the two-sample t-test for independent samples?

Accepted Answer

To estimate the common variance when population variances are assumed equal

Question 8

Given two teaching methods with sample variances $$s_1^2 = 70.661$ and s_2$^2 = 85.378$$, and $$n_1$$ = $$n_2 = 10$, what is the pooled variance?

Accepted Answer

$$ s_p^2$ = \frac{70.661 + 85.378}{2} = 78.0195 $$

Question 9

Which formula is used to calculate the test statistic for a paired (dependent) samples t-test?

Accepted Answer

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

Question 10

In a paired samples t-test, what is the degrees of freedom?

Accepted Answer

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

Question 11

A psychologist tests siblings at the same age on a cognitive task. What type of samples are these?

Accepted Answer

Dependent samples

Question 12

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

Accepted Answer

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

Question 13

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

Accepted Answer

It overestimates the standard error because it ignores the covariance between paired scores

Question 14

Which of the following is TRUE about the t-distribution compared to the z-distribution?

Accepted Answer

The t-distribution is flatter and has thicker tails, especially for small sample sizes

Question 15

A researcher wants to test if a new teaching method improves scores compared to the traditional method. Which hypothesis test should be used if the sample sizes are small and variances are unknown?

Accepted Answer

Two-sample t-test for independent samples

Question 16

If the population variances are not equal, which formula should be used for the standard error in a two-sample t-test?

Accepted Answer

$$ SE = \sqrt{\frac{s_1$^2}{n_1$} + \frac{s_2$^2}{n_2$}} $$

Question 17

Which of the following is NOT an assumption of the two-sample t-test for independent samples?

Accepted Answer

Samples are dependent

Question 18

What is the main purpose of creating difference scores in a paired samples t-test?

Accepted Answer

To account for the dependency between paired observations

Question 19

In a two-sample t-test, if $$n_1 = 15$ and n_2$ = 20$$, what are the degrees of freedom if variances are assumed equal?

Accepted Answer

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

Question 20

A matched samples design is used to compare the effect of a treatment. Which test is most appropriate?

Accepted Answer

Paired samples t-test

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

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