Q: A researcher wants to test if the average number of hours college students sleep per night is different from 7 hours. Which of the following is the correct null and alternative hypothesis for a two-sided test?

$$H_0$$: \mu = 7$$, H_a$$: \mu \neq 7$$

Q: Which of the following is TRUE about the relationship between confidence intervals and two-sided significance tests?

If the p-value is less than $$\alpha$$, the $$(1-\alpha)\times 100\%$$ confidence interval does not contain the null value.

Question 1

Which of the following is a key assumption for conducting a significance test for the population mean when the sample size is small?

Accepted Answer

The population must be normally distributed with no heavy skew or outliers.

Question 2

A researcher wants to test if the average number of hours college students sleep per night is different from 7 hours. Which of the following is the correct null and alternative hypothesis for a two-sided test?

Accepted Answer

$$H_0$$: \mu = 7$$, H_a$$: \mu 
eq 7$$

Question 3

Given a sample mean of $$46,000$$, a hypothesized mean of $$45,000$$, a sample standard deviation of $$4,000$$, and a sample size of $$50$$, what is the value of the test statistic for testing $$H_0$$: \mu = 45,000$$?

Accepted Answer

$$t = \frac{46,000 - 45,000}{4,000/\sqrt{50}} = 1.77$$

Question 4

A p-value is best described as:

Accepted Answer

The probability of observing a test statistic as extreme or more extreme than the one observed, assuming the null hypothesis is true.

Question 5

If a 95% confidence interval for the mean salary is $$(44,891.26, 47,108.74)$$, and you are testing $$H_0$$: \mu = 45,000$$ vs H_a$$: \mu \u003e 45,000$$ at $$\alpha = 0.05$$, what can you conclude?

Accepted Answer

You cannot reject $$H_0$$ because the confidence interval is two-sided and the test is one-sided.

Question 6

Which of the following best describes a Type I error in the context of a criminal trial?

Accepted Answer

Convicting an innocent person.

Question 7

What is the effect of increasing the sample size on the p-value, assuming the observed effect size remains the same?

Accepted Answer

The p-value decreases, making it easier to find statistical significance.

Question 8

In the context of comparing two independent proportions, which of the following is the correct formula for the standard error of the difference in sample proportions?

Accepted Answer

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

Question 9

Refer to the boxplot comparing email hours per week for 18 and 30 year olds. What statistical concern is raised by the presence of an outlier in the 18-year-old group?

Accepted Answer

The assumption of normality may be violated, making t-procedures unreliable.

Question 10

Given the permutation test histogram for the difference in sample means, what does a p-value of 0.0253 indicate?

Accepted Answer

There is strong evidence that the population mean for group 1 is less than group 2.

Question 11

Which of the following is TRUE about the relationship between confidence intervals and two-sided significance tests?

Accepted Answer

If the p-value is less than $$\alpha$$, the $$(1-\alpha)	imes 100\%$$ confidence interval does not contain the null value.

Question 12

Which of the following is a correct interpretation of a 95% confidence interval for the difference in means between two groups?

Accepted Answer

We are 95% confident that the true difference in population means lies within the interval.

Question 13

In a matched pairs (dependent samples) t-test, what is the parameter of interest?

Accepted Answer

The mean of the differences between paired observations.

Question 14

Which of the following is a key assumption for the McNemar test?

Accepted Answer

The sum of discordant pairs (YN + NY) must be at least 30.

Question 15

Which of the following best describes the purpose of a permutation test?

Accepted Answer

To create a sampling distribution by randomly re-assigning data into groups under the null hypothesis.

Question 16

A significance test for comparing two independent means yields a p-value of 0.8248. What is the correct conclusion at $$\alpha = 0.05$$?

Accepted Answer

Fail to reject the null hypothesis; there is no significant evidence of a difference.

Question 17

Which of the following is an example of a Type II error in the context of testing if the average work week is different from 40 hours?

Accepted Answer

Concluding the average work week is not different from 40 hours when it actually is.

Comparing Two Groups: Means, Proportions, and Dependent Samples in Statistical Inference

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