Question 1

The scatter diagram below shows a negative relationship between two variables. Which of the following best describes the correlation and its likely cause?

[Refer to the first image]

A group of students' test scores (y) and the amount of loose pocket change they have (x) are plotted.

Accepted Answer

There is a negative correlation likely due to coincidence.

Question 2

Given the following data for companies' total sales and profits, what type of correlation is most likely present between sales and profits?

Company: Adams (9.5, 0.5), Browns (22.0, 1.4), Clay (35.0, 1.8), Donners (64.0, 3.0), Esters (27.5, 0.9), Framer (45.0, 2.6), Gillies (15.0, 0.8), Hays (57.0, 2.2)

Accepted Answer

Positive correlation

Question 3

Does the correlation coefficient $$r$$ change if you interchange the variables $$x$$ and $$y$$?

Accepted Answer

No, $$r$$ remains the same.

Question 4

Given a correlation coefficient $$r = 0.8$$ for a scatter diagram comparing stock prices ($$y) $$and U.S. employment ($$x$$), how much of the variation in stock price can be accounted for by the best-fit line?

Accepted Answer

$$r^2 = 0.64$, or 64\% of the variation

Question 5

Given a correlation coefficient $$r = -0.95$$ for a scatter diagram comparing the prices of an item ($$y) $$and its availability ($$x$$), how much of the variation in price can be accounted for by the best-fit line?

Accepted Answer

$$r^2 = 0.9025$, or 90.25\% of the variation

Question 6

If a data set has a correlation coefficient $$r = 0.8$$, what percentage of the variation can be accounted for by the best-fit line?

Accepted Answer

$$r^2 = 0.64$, or 64\% of the variation

Question 7

The scatter diagram and best-fit line below show the data for the price of a stock ($$y) $$and U.S. Employment ($$x). $$The correlation coefficient $$r is 0.8. $$Predict the stock price for an employment value of 5.

[Refer to the second image]

Accepted Answer

Approximately 5.5

Question 8

A college requires scholarship students to maintain a GPA of 3.3. GPAs are normally distributed with a mean of 3.0 and a standard deviation of 0.6. What percentile must scholarship students remain in?

Accepted Answer

About the 69th percentile

Question 9

The heights of a large population of students have a mean of 60 inches and a standard deviation of 4 inches. What is the mean of the distribution of sample means for $$n = 16$$?

Accepted Answer

$$60$$

Question 10

If you flip a coin three times, what is the probability of getting at least one head?

Accepted Answer

$$\frac{7}{8}$$

Question 11

If two balanced dice are rolled, what is the probability that the sum of the dice is 9?

Accepted Answer

$$\frac{4}{36}$$

Question 12

A bag contains 6 red marbles, 3 blue marbles, and 5 green marbles. If a marble is randomly selected, what is the probability that it is blue?

Accepted Answer

$$\frac{3}{14}$$

Question 13

If $$P(A) = \frac{6}{11}$$, find $$P(\overline{A}).$$

Accepted Answer

$$\frac{5}{11}$$

Question 14

In a game, you have a $$\frac{1}{22}$$ probability of winning $$89 and a $$\frac{21}{22}$$ probability of losing 9. $$What is your expected value?

Accepted Answer

$$-5.00$$

Question 15

Suppose you pay $$1.00 to roll a fair die and get back 3.00 $$for rolling a 1 or a 2, nothing otherwise. What is your expected value of your gain or loss?

Accepted Answer

$$0.00$$

Question 16

Are the following processes independent or dependent? Four successive jacks are drawn (with replacement) from a regular deck.

Accepted Answer

Independent

Question 17

In one town, 37\% of all voters are Democrats. If two voters are randomly selected for a survey, what is the probability that both are Democrats? (Express answer as a decimal.)

Accepted Answer

0.1369

Question 18

A manufacturing process has a 70\% yield. If five products are randomly selected, what is the probability that all are acceptable? (Express answer as a decimal.)

Accepted Answer

0.16807

Question 19

You are dealt two cards successively (without replacement) from a shuffled deck of 52 playing cards. What is the probability that both cards are red? (Express answer as a decimal.)

Accepted Answer

0.2451

Question 20

You are dealt two cards successively (without replacement) from a shuffled deck of 52 playing cards. What is the probability that both cards are jacks? (Express answer as a decimal.)

Accepted Answer

0.0045

Question 21

The lifetimes of light bulbs of a particular type are normally distributed with a mean of 350 hours and a standard deviation of 6 hours. What percentage of light bulbs have a lifetime that lies within 1 standard deviation to either side of the mean? (Use the 68-95-99.7 rule.)

Accepted Answer

68\%

Statistics Test 2 Review – Step-by-Step Study Guidance

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