Question 1

A company wants to test if a new training program increases employee productivity. They randomly assign employees to either the new program or the standard program and measure their productivity after training. Which statistical test is most appropriate to compare the mean productivity between the two groups?

Accepted Answer

A two-sample t-test

Question 2

Which of the following is the correct formula for the standard error of the difference between two independent sample means, using sample standard deviations?

Accepted Answer

$$SE(\overline{y}_1 - \overline{y}_2) = \sqrt{\frac{s_1$^2}{n_1$} + \frac{s_2$^2}{n_2$}}$$

Question 3

Which assumption is NOT required for the two-sample t-test?

Accepted Answer

The variances of the two groups are equal

Question 4

A researcher collects 'before and after' cholesterol levels from the same patients to test a new medication. Which method should be used to analyze the mean difference?

Accepted Answer

Paired t-test

Question 5

Given the following data for two websites: $$n_1 = 80$$, \overline{y}_1 = 7.7, $$s_1 = 4.6$ and n_2$ = 95, \overline{y}_2 = 7.3, s_2$ = 4.3$$, what is the estimated standard error for the difference in mean page views?

Accepted Answer

$$SE = \sqrt{\frac{4.6^2$}{80} + \frac{4.3^2$}{95}}$$

Question 6

Which of the following best describes the null hypothesis for a two-sample t-test comparing two means?

Accepted Answer

$$H_0$$: \$$mu_1$$ - \$$mu_2 = 0$

Question 7

When is it appropriate to use the pooled t-test instead of the standard two-sample t-test?

Accepted Answer

When the variances of the two populations are equal

Question 8

A 95% confidence interval for the difference in means between two groups is (–0.938, 1.738). What does this interval suggest about the null hypothesis that the means are equal?

Accepted Answer

We cannot reject the null hypothesis because 0 is within the interval

Question 9

Which formula gives the pooled standard error for the difference between two means?

Accepted Answer

$$SE_{pooled}(\overline{y}_1 - \overline{y}_2) = s_{pooled} \sqrt{\frac{1}{n_1$} + \frac{1}{n_2$}}$$

Question 10

Which of the following is NOT a condition for using the paired t-test?

Accepted Answer

The two groups must be independent

Question 11

A study measures the price offered for a used camera by two groups: buying from a friend and buying from a stranger. Which test should be used if the variances are assumed equal?

Accepted Answer

Pooled t-test

Question 12

Which of the following statements is TRUE regarding the use of pooled t-tests?

Accepted Answer

Pooling should only be used when the equal variances assumption is met

Question 13

What is the formula for the confidence interval for the difference between two independent means?

Accepted Answer

$$(\overline{y}_1 - \overline{y}_2) \pm t^* \cdot SE(\overline{y}_1 - \overline{y}_2)$$

Question 14

Which of the following is a correct interpretation of a P-value of 0.041 in a paired t-test at $$\alpha = 0.05$$?

Accepted Answer

There is sufficient evidence to reject the null hypothesis

Question 15

Why is it important to check for outliers and non-normality when using paired t-methods?

Accepted Answer

Because outliers and non-normality can affect the validity of the test results

Question 16

Which of the following is the formula for the test statistic in a paired t-test?

Accepted Answer

$$t = \frac{\overline{d} - \$$Delta_0$$}{SE(\overline{d})}$$

Comparing Two Means: Two-Sample and Paired t-Methods

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