Question 1

A researcher wants to construct a 95% confidence interval for a population mean using a sample of 8 observations. Which critical value should be used?

Accepted Answer

$$t = 2.306$$

Question 2

Which formula is used to calculate the margin of error for a confidence interval for a population proportion?

Accepted Answer

$$E = z^* \sqrt{\dfrac{p(1-p)}{n}}$$

Question 3

A sociologist wants to test if the proportion of females aged 15 and under living alone has changed from 58% in 2000. Which null hypothesis should be used?

Accepted Answer

$$H_0$$: p = 0.58$$

Question 4

In a random sample of 474 adult males, 32 are found to have hypertension. What is the point estimate for the proportion of adult males with hypertension?

Accepted Answer

$$\hat{p} = \dfrac{32}{474}$$

Question 5

Which test should be used to compare the mean reading speed before and after a reading course for the same group of students?

Accepted Answer

Paired (dependent) t-test

Question 6

A 95% confidence interval for the mean diameter of Douglas fir trees is $$(192.03, 147.83). $$What does this interval mean?

Accepted Answer

We are 95% confident the true mean diameter of Douglas fir trees is between 147.83 cm and 192.03 cm.

Question 7

Which formula is used to calculate the required sample size for estimating a population proportion with a specified margin of error $$E$$ and confidence level $$z^*$$?

Accepted Answer

$$n = \dfrac{z$$^{*2}$$ p(1-p)}{E^2$}$$

Question 8

A website claims that 95% of its users are satisfied. In a sample of 500 users, 482 are satisfied. What is the sample proportion?

Accepted Answer

$$\hat{p} = \dfrac{482}{500}$$

Question 9

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

Accepted Answer

Rejecting a true null hypothesis

Question 10

A researcher wants to compare the mean swimming times of two independent groups: one using goggles and one not. Which test should be used?

Accepted Answer

Two-sample t-test

Question 11

Which formula is used to calculate the standard error of the difference between two independent sample means?

Accepted Answer

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

Question 12

A study finds that the mean reading speed increased after a course. The p-value is 0.0033 and the significance level is 0.10. What is the correct conclusion?

Accepted Answer

Reject the null hypothesis; there is evidence the mean reading speed increased.

Question 13

Which plot is most appropriate to check the normality of a sample before conducting a t-test?

Accepted Answer

Normal probability plot

Question 14

A 95% confidence interval for the difference in mean productivity between two drugs is $$(0.057, 0.049). $$What does this interval suggest?

Accepted Answer

There is no significant difference in mean productivity between the two drugs.

Question 15

Which of the following is the correct null hypothesis for testing if the mean arrival and departure speeds are equal for two independent samples?

Accepted Answer

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

Question 16

A sample of 25 swimmers using new goggles had a mean time of 14.43 seconds with a standard deviation of 0.98 seconds. What is the standard error of the mean?

Accepted Answer

$$SE = \dfrac{0.98}{\sqrt{25}}$$

Question 17

Which of the following is a correct interpretation of a p-value?

Accepted Answer

The probability of observing the sample data, or something more extreme, if the null hypothesis is true.

Question 18

A researcher wants to estimate the proportion of adults with hypertension to within 4 percentage points with 95% confidence. Which formula should be used to determine the required sample size?

Accepted Answer

$$n = \dfrac{z$$^{*2}$$ p(1-p)}{E^2$}$$

Question 19

Which hypothesis is a statement of no change?

Accepted Answer

Null hypothesis ($$H_0)$$

Confidence Intervals and Hypothesis Testing: Study Guide for Chapters 9, 10, and 11

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