Q: A researcher is testing whether a new medication lowers blood pressure more than the current standard. Which is the correct alternative hypothesis for a lower-tail test?

$$H_1$$: \mu_{\text{new}} \u003c \mu_{\text{standard}}$$

Question 1

A company wants to compare the average sales performance of two different sales teams. Which of the following is the correct null hypothesis for a two-tailed test comparing the means of the two teams?

Accepted Answer

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

Question 2

A researcher is testing whether a new medication lowers blood pressure more than the current standard. Which is the correct alternative hypothesis for a lower-tail test?

Accepted Answer

$$H_1$$: \mu_{	ext{new}} \u003c \mu_{	ext{standard}}$$

Question 3

You are given two independent samples with unknown and unequal variances. Which t-test should you use to compare their means in Excel?

Accepted Answer

Two-Sample Assuming Unequal Variances

Question 4

A marketing manager wants to know if the proportion of customers who prefer Brand A is different between two cities. Which is the correct null hypothesis for this test?

Accepted Answer

$$H_0$$: $$p_1$$ = $$p_2$$

Question 5

In a paired t-test, which of the following scenarios is most appropriate?

Accepted Answer

Comparing the test scores of students before and after a training program

Question 6

A company wants to compare the mean productivity of three different manufacturing plants. Which statistical test should be used?

Accepted Answer

ANOVA (Analysis of Variance)

Question 7

If the p-value from an ANOVA test is less than 0.05, what is the correct interpretation?

Accepted Answer

At least one population mean is significantly different from the others.

Question 8

Which formula is used to calculate the test statistic for a two-sample t-test assuming equal variances?

Accepted Answer

$$t = \frac{\bar{x}_1 - \bar{x}_2}{s_p \sqrt{\frac{1}{n_1$} + \frac{1}{n_2$}}}$$

Question 9

A hospital wants to test if the recovery rate for a new treatment is higher than the standard treatment. They collect data and perform a hypothesis test for two proportions. Which formula should they use for the test statistic?

Accepted Answer

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

Question 10

A business analyst is comparing the mean monthly expenses of two branches using a two-sample t-test. The p-value is 0.12. What should the analyst conclude at a 5% significance level?

Accepted Answer

There is not enough evidence to conclude a significant difference in mean expenses.

Question 11

Which of the following is an assumption of the ANOVA test?

Accepted Answer

The populations have equal variances.

Question 12

A researcher collects before-and-after data on the same group of patients to test the effect of a new diet. Which test should be used?

Accepted Answer

Paired Two Sample for Means t-test

Question 13

Which of the following is NOT a correct interpretation of a p-value?

Accepted Answer

The probability that the null hypothesis is true.

Question 14

A company tests whether the mean delivery time differs among four shipping providers. The ANOVA test returns a significant result. What should the company do next?

Accepted Answer

Conduct post-hoc tests to determine which means differ.

Question 15

Which of the following is the correct formula for the pooled variance $$s_p^2$ used in the two-sample t-test assuming equal variances?

Accepted Answer

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

Question 16

A study compares the mean test scores of students from three different schools. The ANOVA test yields a p-value of 0.03. What is the correct conclusion at the 0.05 significance level?

Accepted Answer

At least one school's mean test score is significantly different from the others.

Question 17

Which of the following situations requires a two-sample t-test assuming unequal variances?

Accepted Answer

Comparing the mean salaries of employees at two companies with different salary variances.

Question 18

A researcher wants to test if the proportion of defective products is higher in Factory A than in Factory B. Which is the correct alternative hypothesis?

Accepted Answer

$$H_1$$: p_A \u003e p_B$$

Question 19

Which of the following is a key assumption for the two-sample t-test assuming equal variances?

Accepted Answer

The two populations have the same variance.

Question 20

A business wants to compare the mean customer satisfaction scores from two independent stores. The sample sizes are small and variances are unknown but assumed equal. Which test should be used?

Accepted Answer

Two-Sample t-Test Assuming Equal Variances

Comparing Means and Proportions: Two-Sample Tests and ANOVA

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