Question 1

A company wants to compare the average monthly sales between two independent store locations. The sample sizes are both 12, and the sample variances are similar. Which test should be used to determine if there is a significant difference in mean sales between the two locations?

Accepted Answer

A pooled-variance t-test

Question 2

Which of the following is an assumption for the pooled-variance t-test when comparing two independent means?

Accepted Answer

The population variances are unknown but assumed equal.

Question 3

A researcher collects data on the effectiveness of two different medications for lowering blood pressure. The samples are independent, and the variances are not assumed to be equal. Which test statistic should be used?

Accepted Answer

A separate-variance t-test

Question 4

Which formula correctly represents the test statistic for the pooled-variance t-test for two independent samples?

Accepted Answer

$$t_{STAT} = \frac{(\overline{X}_1 - \overline{X}_2) - (\mu_1$ - \mu_2$)}{\sqrt{S_p^2$ \left( \frac{1}{n_1$} + \frac{1}{n_2$} \right)}}$$

Question 5

A marketing team wants to compare the proportion of customers who made a purchase after seeing two different advertisements. Which test is most appropriate?

Accepted Answer

A two-sample z-test for proportions

Question 6

Which of the following is the correct formula for the pooled estimate of the overall proportion when testing the difference between two population proportions?

Accepted Answer

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

Question 7

A company wants to test if the variance in monthly sales is different between two stores. The sample variances are $$S_1^2 = 50$ and S_2$^2 = 20$$, each with 15 observations. What is the correct test statistic to use?

Accepted Answer

$$F = \frac{S_1$^2}{S_2$^2}$$

Question 8

Which of the following is NOT an assumption required for the one-way ANOVA F test?

Accepted Answer

The sample means must be equal.

Question 9

In a one-way ANOVA, what does the F statistic represent?

Accepted Answer

The ratio of the mean square among groups to the mean square within groups.

Question 10

A researcher is comparing the mean test scores of students from three different teaching methods. Which statistical test should be used?

Accepted Answer

One-way ANOVA

Question 11

Which formula correctly represents the confidence interval for the difference between two independent means with equal variances?

Accepted Answer

$$(\overline{X}_1 - \overline{X}_2) \pm t_{\alpha/2} \sqrt{S_p^2$ \left( \frac{1}{n_1$} + \frac{1}{n_2$} \right)}$$

Question 12

A paired difference t-test is most appropriate in which scenario?

Accepted Answer

Comparing the weights of patients before and after a diet program.

Question 13

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

Accepted Answer

$$t_{STAT} = \frac{\overline{D} - \mu_D}{S_D / \sqrt{n}}$$

Question 14

A company is testing whether the proportion of customers who buy a product is different between two regions. The sample sizes are large. Which formula should be used for the test statistic?

Accepted Answer

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

Question 15

Which of the following best describes the purpose of the Tukey-Kramer procedure in ANOVA?

Accepted Answer

To determine which specific group means are significantly different after finding a significant F statistic.

Question 16

If the Levene test for homogeneity of variance is significant, what does this imply about the ANOVA assumptions?

Accepted Answer

The assumption of equal variances is violated.

Question 17

Which of the following is the correct formula for the confidence interval for the difference between two population proportions?

Accepted Answer

$$(p_1$ - p_2$) \pm z_{\alpha/2} \sqrt{\frac{p_1$(1-p_1$)}{n_1$} + \frac{p_2$(1-p_2$)}{n_2$}}$$

Question 18

A business analyst wants to compare the mean customer satisfaction scores from four different branches of a retail chain. Which statistical method should be used?

Accepted Answer

One-way ANOVA

Two-Sample Tests and One-Way ANOVA: Comparing Means, Proportions, and Variances

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