Question 1

A botanist wants to test whether the mean nitrogen content in leaves from a wildflower species differs from 3.0%. She collects a random sample of 15 leaves and finds a sample mean of 2.94% with a standard deviation of 0.15%. Which test statistic should she use to test $$H_0$$: \mu = 3.0$$ versus H_a$$: \mu 
eq 3.0$$?

Accepted Answer

$$t = \frac{\bar{x} - \mu_0$}{s/\sqrt{n}}$$

Question 2

Which of the following is an assumption for the one-sample t-test for a mean?

Accepted Answer

The sample observations are independent of one another.

Question 3

A quality control engineer wants to test if the variance in spring length is greater than 0.04. She collects a sample of 9 springs and finds a sample variance of 0.06. Which test should she use?

Accepted Answer

Chi-square test for a variance

Question 4

Which formula gives the confidence interval for the population mean $$\mu$$ when the population variance is unknown?

Accepted Answer

$$\bar{x} \pm t_{n-1,1-\alpha/2} \frac{s}{\sqrt{n}}$$

Question 5

A researcher compares the effectiveness of two advertising campaigns by randomly assigning 20 regions to each campaign and measuring sales. Which test should be used if the population variances are not equal?

Accepted Answer

Welch's (nonpooled) t-test

Question 6

Which formula is used to calculate the test statistic for the F-test comparing two sample variances $$s_1^2$ and s_2$^2$$?

Accepted Answer

$$F = \frac{s_1$^2}{s_2$^2}$$

Question 7

In a matched-pairs experiment, what is the correct null hypothesis to test if the average difference between paired observations is zero?

Accepted Answer

$$H_0$$: \mu_d = 0$$

Question 8

A medical researcher wants to compare the mean blood pressure before and after a treatment in the same group of patients. Which statistical test is most appropriate?

Accepted Answer

Matched-pairs t-test

Question 9

Which of the following is NOT an assumption of the Student's (pooled) t-test for two independent samples?

Accepted Answer

The two samples are paired.

Question 10

Suppose you want to estimate the ratio of two population variances with a 95% confidence interval. Which formula should you use?

Accepted Answer

$$\left( \frac{s_1$^2}{s_2$^2} \right) \left( \frac{1}{F_{1-\alpha/2, n_1$-1, n_2$-1}}, \frac{1}{F_{\alpha/2, n_1$-1, n_2$-1}} \right)$$

Question 11

A study tests whether a new teaching method improves reading scores compared to the standard method using pairs of students with similar initial scores. Which test is most appropriate?

Accepted Answer

Matched-pairs t-test

Question 12

Which formula gives the test statistic for Welch's (nonpooled) t-test for two independent samples with 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 13

Which of the following scenarios is most appropriate for a one-sample t-test for a mean?

Accepted Answer

Testing if the average caffeine content in a new energy drink is 80 mg per can.

Question 14

Which of the following is a correct interpretation of a 95% confidence interval for a mean?

Accepted Answer

We are 95% confident that the interval contains the true population mean.

Question 15

A biologist wants to test if the variance in enzyme activity differs between two species. She collects 10 samples from each species. Which test should she use?

Accepted Answer

F-test for equality of variances

Question 16

Which of the following is a key assumption for the F-test for equality of variances?

Accepted Answer

Both populations are normally distributed.

Question 17

A company tests whether a new process reduces the standard deviation of product weight below 2 grams. Which hypothesis test should be used?

Accepted Answer

Chi-square test for a variance

Question 18

Which formula gives the test statistic for the matched-pairs t-test?

Accepted Answer

$$t = \frac{\bar{x}_d}{s_d/\sqrt{n}}$$

Methods for Quantitative Response Variables – One and Two Groups

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