Question 1

A nutritionist wants to estimate the average grams of protein in a brand of protein bars. She takes a random sample of 40 bars with a sample mean of 210g and knows from prior data that the population standard deviation is 12g. What is the correct formula for the margin of error for a 95% confidence interval in this scenario?

Accepted Answer

$$E = z_{\alpha/2} \cdot \frac{\sigma}{\sqrt{n}}$$

Question 2

Which of the following best describes the interpretation of a 95% confidence interval for a population mean?

Accepted Answer

We are 95% confident that the interval calculated from our sample contains the true population mean.

Question 3

A researcher wants to estimate the average amount of time college students spend exercising per day. She wants a 95% confidence interval with a margin of error no greater than 3 minutes. Prior studies suggest $$\sigma = 12$$ minutes. What is the minimum sample size required?

Accepted Answer

$$n = \left( \frac{z_{\alpha/2} \cdot \sigma}{E} \$$right)^2$$

Question 4

Which of the following scenarios requires the use of the t-distribution rather than the z-distribution for constructing a confidence interval for the mean?

Accepted Answer

The population standard deviation is unknown and the sample size is 20.

Question 5

A school administrator wants to compare the proportion of students who passed a standardized math exam in two different schools. In Class A, 72 out of 120 students passed; in Class B, 65 out of 100 students passed. What is the correct formula for the test statistic to test for a difference in proportions?

Accepted Answer

$$z = \frac{(\hat{p}_1 - \hat{p}_2) - 0}{\sqrt{\hat{p}(1-\hat{p})\left(\frac{1}{n_1$} + \frac{1}{n_2$}\right)}}$$

Question 6

A company is comparing the average number of hours worked per week by employees at two companies. Company A: $$n_1 = 25$, $$\bar{x}_1 = 22.4$$, s_1$ = 3.2$$; Company B: $$n_2 = 16$, $$\bar{x}_2 = 21.1$$, s_2$ = 2.9. $$What is the correct formula for the test statistic for the difference in means (assuming unequal variances)?

Accepted Answer

$$t = \frac{(\bar{x}_1 - \bar{x}_2)}{\sqrt{\frac{s_1$^2}{n_1$} + \frac{s_2$^2}{n_2$}}}$$

Question 7

Which of the following is always true about the F-distribution?

Accepted Answer

It is always right-skewed and takes only positive values.

Question 8

In a two-sample hypothesis test for variance, what does an F-statistic near 1 indicate?

Accepted Answer

The two sample variances are approximately equal.

Question 9

A psychologist is interested in whether increased time spent on hobbies reduces reported stress level. She finds a correlation coefficient $$r = -0.65$$ with a p-value of 0.02. What is the correct interpretation?

Accepted Answer

There is a significant negative linear correlation between time spent on hobbies and stress level.

Question 10

Which of the following is a correct null hypothesis for a two-sample test for the difference in population means?

Accepted Answer

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

Question 11

A matched pairs study is conducted to test the effect of a new medication on blood pressure. The sample mean difference is $$\bar{d} = 3.2$$, $$s_d = 6.7$$, $$n = 37. $$What is the correct formula for the test statistic?

Accepted Answer

$$t = \frac{\bar{d} - \mu_d}{s_d / \sqrt{n}}$$

Question 12

Which of the following is NOT a condition for constructing a confidence interval for the difference in two proportions?

Accepted Answer

The population variances are equal.

Question 13

A bookstore wants to estimate the average length of books in its adult fiction section. The longest book is 697 pages and the shortest is 298 pages. Using the range rule of thumb, what is the estimated sample standard deviation?

Accepted Answer

$$s \approx \frac{	ext{range}}{4}$$

Question 14

Which of the following best describes a matched pairs design?

Accepted Answer

Each subject is measured twice, or pairs of related subjects are compared.

Question 15

A human resources department is comparing two employee training programs to see if they lead to different pass rates. In Program A, 16 out of 20 employees passed; in Program B, 30 out of 40 passed. Are the basic conditions met to conduct a 2-proportion hypothesis test?

Accepted Answer

Yes, the basic conditions are met.

Question 16

Which of the following is the correct formula for the degrees of freedom for a one-sample t-test?

Accepted Answer

$$df = n - 1$$

Inferring Population Means and Comparing Groups: Confidence Intervals, Hypothesis Tests, and Variance Analysis

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