Q: Which of the following is a correct decision rule for a right-tailed z-test at significance level $$\alpha$$?

Reject $$H_0 if$$ $$z_{\text{stat}} \u003e z_{\alpha}$$

Question 1

Which of the following is the correct formula for the standard error of the difference between two independent sample means when the population standard deviations are known?

Accepted Answer

$$\sigma_{\bar{x}_1-\bar{x}_2} = \sqrt{\frac{\sigma_1^2}{n_1} + \frac{\sigma_2^2}{n_2}}$$

Question 2

A business analyst wants to test if the average time to process an order is different between two warehouses. The population standard deviations are known. Which test statistic should be used?

Accepted Answer

$$z = \frac{(\bar{x}_1 - \bar{x}_2) - (\mu_1 - \mu_2)_{H_0}}{\sqrt{\frac{\sigma_1^2}{n_1} + \frac{\sigma_2^2}{n_2}}}$$

Question 3

Suppose you are comparing the mean spending of two groups with unknown but equal population variances. Which formula should you use for the pooled variance?

Accepted Answer

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

Question 4

A researcher wants to test if the mean length of playoff games is longer than regular season games. Which is the correct set of hypotheses for this right-tailed test?

Accepted Answer

$$H_0: \mu_1 - \mu_2 \leq 0, \quad H_1: \mu_1 - \mu_2 \u003e 0$$

Question 5

When comparing two population proportions, which formula is used to calculate the pooled sample proportion?

Accepted Answer

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

Question 6

A company wants to test if the proportion of younger customers using online banking is higher than that of older customers. Which is the correct test statistic?

Accepted Answer

$$z = \frac{(\hat{p}_1 - \hat{p}_2) - (p_1 - p_2)_{H_0}}{\sqrt{\hat{p}(1-\hat{p})\left(\frac{1}{n_1} + \frac{1}{n_2}\right)}}$$

Question 7

Which of the following is a correct decision rule for a right-tailed z-test at significance level $$\alpha$$?

Accepted Answer

Reject $$H_0 if$$ $$z_{	ext{stat}} \u003e z_{\alpha}$$

Question 8

In a two-sample t-test with equal but unknown variances, what is the correct formula for the degrees of freedom?

Accepted Answer

$$df = n_1 + n_2 - 2$$

Question 9

A confidence interval for the difference between two means does NOT include zero. What does this imply?

Accepted Answer

There is evidence of a significant difference between the two population means.

Question 10

Which of the following is an assumption for using the two-sample t-test with independent samples and unknown but equal variances?

Accepted Answer

Both populations are normally distributed or both sample sizes are at least 30.

Question 11

A study compares the average time to pass through airport security in two cities using independent samples. The sample standard deviations are used in the test. Which distribution should be used to determine the critical value?

Accepted Answer

Student's t-distribution

Question 12

If the p-value for a two-sample z-test is 0.022 and $$\alpha = 0.05$$, what is the correct conclusion?

Accepted Answer

Reject the null hypothesis.

Question 13

Which of the following scenarios requires the use of a paired (dependent) samples t-test?

Accepted Answer

Comparing the mean blood pressure of patients before and after taking medication.

Question 14

Which formula is used to calculate the test statistic for comparing two population proportions?

Accepted Answer

$$z = \frac{(\hat{p}_1 - \hat{p}_2) - (p_1 - p_2)_{H_0}}{\sqrt{\hat{p}(1-\hat{p})\left(\frac{1}{n_1} + \frac{1}{n_2}\right)}}$$

Question 15

A hypothesis test for the difference in means yields a test statistic of $$z = 2.3$$ and a critical value of $$z_{\alpha} = 2.05$$ for a right-tailed test. What is the correct conclusion?

Accepted Answer

Reject the null hypothesis.

Question 16

Which of the following is NOT a step in the hypothesis testing procedure for comparing two means?

Accepted Answer

Calculate the sample median for each group.

Hypothesis Testing for Two Samples: Means and Proportions

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