Q: The scores on a statistics exam are normally distributed with mean 84.5 and standard deviation 6. What is the minimum test score a student must have to be in the top 5%?

$$84.5 + 1.645 \times 6 = 94.37$$

Q: A random sample of 26 test grades has a mean of 84.7 and a standard deviation of 3.6. What is the 95% confidence interval for the mean test grade? (Use $$t_{0.025,25} \approx 2.060)$$

$$84.7 \pm 2.060 \times \frac{3.6}{\sqrt{26}}$$

Q: Given the least squares regression equation $$y = 12.5x + 180$$, what is the predicted number of calories for a hamburger with 28 grams of fat?

$$y = 12.5 \times 28 + 180 = 530$$

Question 1

Which of the following sampling techniques involves dividing the population into subgroups and then randomly selecting members from each subgroup?

Accepted Answer

Stratified sampling

Question 2

A researcher records the number of books read by students in a month. What is the level of measurement for this data?

Accepted Answer

Ratio

Question 3

A frequency distribution has class limits 10-19, 20-29, 30-39, and so on. If the lowest value is 10 and the highest is 79, what is the class width?

Accepted Answer

$$10$$

Question 4

Given the data set: 5, 7, 7, 8, 10, what is the standard deviation?

Accepted Answer

$$1.789$$

Question 5

A survey of 250 students at a university found that 70% owned a laptop. What is the population in this context?

Accepted Answer

All students at the university

Question 6

Suzanne owns a diner. Last week, 230 people walked by, and 150 entered. What is the probability that a person who walks by will enter the diner?

Accepted Answer

$$\frac{150}{230}$$

Question 7

A bag contains 8 white, 4 black, 12 red, and 6 blue beads. If two beads are drawn with replacement, what is the probability that both are red? (Round to 4 decimal places)

Accepted Answer

$$\left(\frac{12}{30}\$$right)^2$$ = 0.16$$

Question 8

From the contingency table, what is the probability that a randomly selected person has a limited text plan?

Accepted Answer

$$\frac{162}{582}$$

Question 9

Which of the following is NOT a property of a binomial probability distribution?

Accepted Answer

The trials are dependent

Question 10

A local survey found that 24% of drivers do not wear a seat belt at all times. In 20 traffic stops, what is the probability that exactly 7 drivers were not wearing a seat belt? (Use the binomial formula)

Accepted Answer

$$\binom{20}{7} (0.24)^7$ (0.76$$)^{13}$$

Question 11

The number of hours of TV watched per day by children ages 7-14 is normally distributed with mean 4.2 and standard deviation 1.8. What is the z-score for a child who watches 5.6 hours per day?

Accepted Answer

$$z = \frac{5.6 - 4.2}{1.8} = 0.778$$

Question 12

The scores on a statistics exam are normally distributed with mean 84.5 and standard deviation 6. What is the minimum test score a student must have to be in the top 5%?

Accepted Answer

$$84.5 + 1.645 	imes 6 = 94.37$$

Question 13

Given the confidence interval $$3.54 \u003c \mu \u003c 7.68$$, $$\sigma = 1.24$$, and $$n = 85$$, what is the margin of error $$E$$?

Accepted Answer

$$E = \frac{7.68 - 3.54}{2} = 2.07$$

Question 14

A random sample of 26 test grades has a mean of 84.7 and a standard deviation of 3.6. What is the 95% confidence interval for the mean test grade? (Use $$t_{0.025,25} \approx 2.060)$$

Accepted Answer

$$84.7 \pm 2.060 	imes \frac{3.6}{\sqrt{26}}$$

Question 15

In a recent survey of 514 SUV owners, 154 said they were satisfied with their gas mileage. What is the point estimate for the proportion of satisfied SUV owners?

Accepted Answer

$$\frac{154}{514}$$

Question 16

Which of the following situations requires the use of a t-interval rather than a z-interval?

Accepted Answer

The population standard deviation is unknown and the sample size is small

Question 17

Which of the following is the correct null hypothesis for testing whether the mean weight of border collies is 46 pounds?

Accepted Answer

$$H_0$$: \mu = 46$$

Question 18

The correlation coefficient between fat grams and calories in hamburgers is found to be $$r = 0.95. $$What does this indicate?

Accepted Answer

There is a strong positive linear relationship between fat grams and calories

Question 19

Given the least squares regression equation $$y = 12.5x + 180$$, what is the predicted number of calories for a hamburger with 28 grams of fat?

Accepted Answer

$$y = 12.5 	imes 28 + 180 = 530$$

Comprehensive Statistics Final Exam Study Guide

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