Q: A random sample of 200 college students found that 120 prefer online classes. Construct a 95% confidence interval for the proportion of students who prefer online classes. (Use $$z^* = 1.96)$$

$$0.60 \pm 1.96 \times \sqrt{\frac{0.60 \times 0.40}{200}}$$

Question 1

Which of the following best describes a Type I error in hypothesis testing?

Accepted Answer

Rejecting the null hypothesis when it is true.

Question 2

Suppose a pharmaceutical company is testing a new drug. The null hypothesis is that the drug has no effect. If the company concludes the drug is effective when it actually is not, what type of error have they made?

Accepted Answer

Type I error

Question 3

Given a sample mean $$\bar{x} = 52$$, population mean $$\mu = 50$$, sample standard deviation $$s = 8$$, and sample size $$n = 16$$, what is the value of the test statistic for a one-sample t-test?

Accepted Answer

$$t = \frac{52 - 50}{8/\sqrt{16}} = 1$$

Question 4

Which of the following is the correct formula for the standard error of the mean when the population standard deviation is unknown?

Accepted Answer

$$SE = \frac{s}{\sqrt{n}}$$

Question 5

A researcher is comparing the mean blood pressure before and after a treatment in the same group of patients. Which test is most appropriate?

Accepted Answer

Paired t-test (dependent samples)

Question 6

If the p-value of a test statistic is 0.04 and the significance level $$\alpha is 0.01$$, what is the correct decision?

Accepted Answer

Fail to reject $$H_0$$

Question 7

Which of the following statements about the relationship between sample size and standard error is correct?

Accepted Answer

As sample size increases, standard error decreases.

Question 8

A 95% confidence interval for a mean is calculated as $$\bar{x} \pm t^* \frac{s}{\sqrt{n}}. If $$the sample size is doubled, what happens to the width of the confidence interval?

Accepted Answer

It decreases, but not by half.

Question 9

Which of the following is an assumption for using a two-sample t-test for independent samples?

Accepted Answer

The two populations have equal variances.

Question 10

Suppose you are testing $$H_0$$: \mu = 100$$ vs H_a$$: \mu 
eq 100$$ at $$\alpha = 0.05$$. Your test statistic is z = 2.1$. What is the correct conclusion?

Accepted Answer

Reject $$H_0$$

Question 11

Which of the following best describes the p-value in hypothesis testing?

Accepted Answer

The probability of obtaining a result as extreme or more extreme than the observed result, assuming the null hypothesis is true.

Question 12

A random sample of 200 college students found that 120 prefer online classes. Construct a 95% confidence interval for the proportion of students who prefer online classes. (Use $$z^* = 1.96)$$

Accepted Answer

$$0.60 \pm 1.96 	imes \sqrt{\frac{0.60 	imes 0.40}{200}}$$

Question 13

Which of the following is the correct rejection region for a two-tailed z-test at $$\alpha = 0.05$$?

Accepted Answer

$$|z| \u003e 1.96$$

Question 14

If the assumptions for a t-test are not met, which of the following is the most appropriate action?

Accepted Answer

Use a nonparametric alternative test.

Question 15

A study finds a p-value of 0.002 for a test at $$\alpha = 0.01. $$What is the correct interpretation?

Accepted Answer

There is strong evidence against the null hypothesis.

Question 16

Which of the following is the correct formula for the test statistic for comparing two means with independent samples and equal variances?

Accepted Answer

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

Question 17

A medical researcher wants to test if a new treatment changes the mean recovery time. Which of the following is the correct set of hypotheses?

Accepted Answer

$$H_0$$: \mu = \$$mu_0$$, $$H_a: \mu 
eq \mu_0$

Question 18

Which of the following is NOT an assumption for the one-sample t-test?

Accepted Answer

The population standard deviation is known.

Question 19

A confidence interval for the mean is given as (45.2, 54.8). What is the sample mean?

Accepted Answer

50.0

Question 20

Which of the following best describes the power of a statistical test?

Accepted Answer

The probability of correctly rejecting a false null hypothesis.

Exam 3 Review: Hypothesis Testing, Confidence Intervals, and Sampling Distributions

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