Question 1

Which of the following scenarios is most appropriate for a hypothesis test for two population means using independent samples?

Accepted Answer

Comparing the average math test scores of students from two different schools.

Question 2

When conducting a hypothesis test for two population means using independent samples and the population standard deviations are unknown, which distribution should be used?

Accepted Answer

The t-distribution.

Question 3

A business analyst wants to compare the mean sales at two stores, A and B, using independent samples. The sample sizes are both 15, and the population standard deviations are unknown. What is the correct formula for the degrees of freedom for the t-test?

Accepted Answer

$$df = n_1$ + n_2$ - 2$$

Question 4

Which of the following is a key assumption when using the two-sample t-test for independent samples with unknown and unequal variances?

Accepted Answer

The samples must be independent.

Question 5

A marketing team tests a new checkout page design by sending 15 users to both the new and old versions and measuring the time spent. Which type of hypothesis test should be used?

Accepted Answer

Paired sample t-test (dependent samples).

Question 6

What is the formula for the t-statistic when comparing two independent sample means with unknown and unequal variances?

Accepted Answer

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

Question 7

In a paired sample t-test, what is the null hypothesis when comparing the mean difference before and after a training program?

Accepted Answer

$$H_0$$: \mu_d = 0$$

Question 8

A company wants to test if the proportion of customers completing purchases is higher with a discount offer. Which test should be used?

Accepted Answer

Test for difference between two population proportions.

Question 9

What is the formula for the z-statistic when testing the difference between two population proportions?

Accepted Answer

$$z = \frac{(p_1$ - p_2$) - (P_1$ - P_2$)}{\sqrt{p(1-p)\left(\frac{1}{n_1$} + \frac{1}{n_2$}\right)}}$$

Question 10

Which condition must be met to use the normal approximation for the difference between two population proportions?

Accepted Answer

Each sample group must have at least 5 successes and 5 failures.

Question 11

A researcher collects data on the time spent watching drama and comedy movies by the same group of users. What is the correct formula for the sample standard deviation of the paired differences?

Accepted Answer

$$s_d = \sqrt{\frac{\sum (d_i - \bar{d})^2$}{n-1}}$$

Question 12

In a paired sample t-test, what is the formula for the t-statistic?

Accepted Answer

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

Question 13

A company wants to estimate the confidence interval for the difference in mean sales between two stores using independent samples. What is the correct formula for the confidence interval?

Accepted Answer

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

Question 14

Which of the following best describes a paired sample?

Accepted Answer

Two samples where each observation in one sample is matched with a specific observation in the other sample.

Question 15

A business wants to test if a new process is more efficient than the old one by measuring the time spent by the same employees before and after the change. Which hypothesis test should be used?

Accepted Answer

Paired sample t-test.

Question 16

If the calculated t-statistic in a two-sample t-test for independent samples is greater than the critical t-value at a significance level of 0.05, what is the correct conclusion?

Accepted Answer

Reject the null hypothesis.

Question 17

In a test for the difference between two population proportions, what is the pooled proportion estimator formula?

Accepted Answer

$$p = \frac{x_1$ + x_2$}{n_1$ + n_2$}$$

Question 18

Which of the following is a reason to use the unequal variance (Welch's) t-test rather than the equal variance t-test in real-world scenarios?

Accepted Answer

We often do not know if population variances are equal.

Hypothesis Testing for Two Population Parameters: Means and Proportions

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