Question 1

Which of the following best describes a confidence interval?

Accepted Answer

A range of values, derived from sample statistics, that is likely to contain the true population parameter with a specified level of confidence.

Question 2

A researcher wants to estimate the average number of hours college students sleep per night. She collects a random sample of 36 students and finds a sample mean of 6.8 hours with a standard deviation of 1.2 hours. What is the 95% confidence interval for the population mean?

Accepted Answer

$$6.8 \pm 1.96 \left( \frac{1.2}{\sqrt{36}} \right)$$, which is (6.41, 7.19)

Question 3

Which of the following statements about the margin of error in a confidence interval is correct?

Accepted Answer

The margin of error decreases as the sample size increases, all else being equal.

Question 4

A study finds that 168 out of 250 randomly sampled US adults carry a balance on their credit cards. What is the 80% confidence interval for the true proportion of US adults who carry a balance? (Use $$z = 1.28$$ for 80% confidence.)

Accepted Answer

$$(0.634, 0.710)$$

Question 5

Which of the following best describes a matched pairs design?

Accepted Answer

A study design where each subject is measured twice, or subjects are paired in a meaningful way, and the differences are analyzed.

Question 6

A clinical trial compares the mean reduction in blood pressure between a new drug and a placebo. The 95% confidence interval for the difference in means is $$(-2.5, 5.0). $$What can be concluded?

Accepted Answer

There is no statistically significant difference in mean reduction between the drug and placebo at the 5% significance level.

Question 7

A 95% confidence interval for the difference in proportions between two years for current smokers is $$(0.042, 0.058). $$What does this interval suggest?

Accepted Answer

There is a statistically significant decline in the proportion of current smokers between the two years.

Question 8

In a study, the 95% confidence interval for the difference in mean housework hours per week between women and men is $$(9.52, 13.48). $$What is the correct interpretation?

Accepted Answer

We are 95% confident that women spend between 9.52 and 13.48 more hours per week on housework than men.

Question 9

A sample of 100 adults finds that 83 believe in life after death. What is the 95% confidence interval for the proportion of adults who believe in life after death? (Use $$z = 1.96.)$$

Accepted Answer

$$(0.804, 0.896)$$

Question 10

A 95% confidence interval for the difference in proportions between active and inactive adults who suffered heart attacks is $$(-0.042, 0.242). $$What does this interval indicate?

Accepted Answer

There is no statistically significant difference in the proportions, since the interval includes zero.

Question 11

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

Accepted Answer

If we were to take many samples and build a confidence interval from each, about 95% of those intervals would contain the true population mean.

Question 12

A sample of 25 hot sauces has a mean spiciness rating of 10 and a standard deviation of 2. What is the 95% confidence interval for the mean spiciness rating?

Accepted Answer

$$(9.446, 10.554)$$

Question 13

Which of the following is NOT a requirement for constructing a confidence interval for a population mean?

Accepted Answer

The population standard deviation must be known.

Question 14

A 95% confidence interval for the mean difference in test scores between two teaching methods is $$(1.2, 4.8). $$What does this suggest?

Accepted Answer

There is a statistically significant difference in mean test scores between the two methods.

Question 15

Which of the following best defines a point estimate?

Accepted Answer

A single value calculated from sample data that serves as a best guess for a population parameter.

Question 16

A 95% confidence interval for the difference in means between two brands of soda for artificial sweetener content is $$(-2.2, 2.5). $$What is the correct conclusion?

Accepted Answer

There is no statistically significant difference in artificial sweetener content between the two brands.

Question 17

Which of the following is a parameter, not a statistic?

Accepted Answer

The mean height of all adult women in the United States.

Question 18

A 95% confidence interval for the proportion of people who support a new policy is $$(0.38, 0.47). $$What does this mean?

Accepted Answer

We are 95% confident that the true proportion of people who support the policy is between 0.38 and 0.47.

Question 19

Which of the following is the correct formula for the standard error (SE) of the difference between two independent sample means?

Accepted Answer

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

Confidence Intervals and Statistical Inference: Study Guide for College Statistics

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