Question 1

Which of the following best describes the null hypothesis ($$H_0) $$when testing whether the mean of population 1 is greater than the mean of population 2?

Accepted Answer

$$H_0$$: \$$mu_1$$ \leq \$$mu_2$$

Question 2

A researcher wants to test if a new training technique increases test scores. Seven students' scores before and after training are compared. Which statistical test is most appropriate?

Accepted Answer

Paired t-test

Question 3

Given two independent samples with sample means $$\bar{x}_1 = 85.6$$, $$\bar{x}_2 = 82.3$$, sample sizes $$n_1 = 8$, n_2$ = 7$$, and sample standard deviations $$s_1 = 6.04$, s_2$ = 5.06$$, what is the correct formula for the standard error of the difference in means?

Accepted Answer

$$SE = \sqrt{\frac{s_1$^2}{n_1$} + \frac{s_2$^2}{n_2$}}$$

Question 4

Suppose you are testing $$H_0$$: $$p_1$$ = $$p_2$$ versus $$H_a: p_1$ 
eq p_2$ for two proportions. Which of the following is the correct test statistic?

Accepted Answer

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

Question 5

A 95% confidence interval for $$\mu_1$ - \mu_2$ is calculated as (0.16$$, 6.78)$$. What is the correct interpretation?

Accepted Answer

We are 95% confident that the true mean difference is between 0.16 and 6.78

Question 6

Which of the following is NOT an assumption for constructing a confidence interval for the difference between two means using independent samples?

Accepted Answer

The two samples are dependent

Question 7

Given the following regression equation: $$y = 1.91x + 5.08$$, what is the predicted value of $$y$$ when $$x = 20$$?

Accepted Answer

$$y = 43.28$$

Question 8

If the calculated $$p-$$value for a hypothesis test is 0.031 and the significance level $$\alpha is 0.05$$, what is the correct decision?

Accepted Answer

Reject $$H_0$$

Question 9

Which of the following best describes the meaning of a significant linear correlation between two variables?

Accepted Answer

There is evidence of a linear relationship between the variables

Question 10

A test for the difference in means between two populations yields a test statistic that falls in the critical region. What is the correct conclusion?

Accepted Answer

Reject the null hypothesis

Question 11

Which of the following is the correct formula for the linear correlation coefficient $$r$$?

Accepted Answer

$$r = \frac{n\sum xy - \sum x \sum y}{\sqrt{[n\sum x^2$ - (\sum x)^2$][n\sum y^2$ - (\sum y)^2$]}}$$

Question 12

In a two-tailed hypothesis test with $$\alpha = 0.05$$, what is the critical value for $$z$$?

Accepted Answer

$$\pm 1.96$$

Question 13

Which of the following statements about $$p-$$values is correct?

Accepted Answer

A small $$p-$$value provides evidence against the null hypothesis

Question 14

A researcher calculates a test statistic of $$t = 2.267$$ with $$df = 12$$ for a two-tailed test at $$\alpha = 0.05. $$The critical value is $$t_{0.025,12} = 2.179. $$What is the correct conclusion?

Accepted Answer

Reject $$H_0$$

Question 15

Which of the following is a correct interpretation of a 99% confidence interval for the difference between two means?

Accepted Answer

We are 99% confident that the interval contains the true difference in population means

Question 16

If the correlation coefficient $$r = 0.837$$ for two variables, what does this indicate?

Accepted Answer

There is a strong positive linear relationship

Question 17

Which of the following is NOT a step in hypothesis testing?

Accepted Answer

Prove the null hypothesis is true

Question 18

A company wants to compare the mean productivity scores of employees before and after a new training program. Which test should be used?

Accepted Answer

Paired t-test

Question 19

Which of the following is the correct formula for the regression line predicting $$y$$ from $$x$$?

Accepted Answer

$$y = b_0$ + b_1x$$

Hypothesis Testing, Confidence Intervals, and Correlation: Study Notes for Statistics Exam Prep

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