Question 1

The scatter diagram below compares students' test scores (y) and the amount of loose pocket change they have (x). What type of correlation is shown, and is it likely due to coincidence, a common underlying cause, or a direct cause?

[Refer to the first image]

Accepted Answer

Negative correlation; likely due to coincidence.

Question 2

Given the following company data, what type of correlation would you expect between total sales and profits?

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

Accepted Answer

Positive correlation

Question 3

Does the correlation coefficient $$r$$ remain unchanged if the variables $$x$$ and $$y$$ are interchanged?

Accepted Answer

Yes, $$r$$ remains unchanged.

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 the availability of that item ($$x$$), 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

64\%

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 $$x = 5$$.

[Refer to the second image]

Accepted Answer

Approximately 6

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

Approximately 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

$$\frac{1}{9}$$

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

$$\frac{1}{4}$$

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

$$-5$$

Question 15

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

Accepted Answer

$$0$$

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 they are both Democrats? Express your 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 of them are acceptable? Express your 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 your answer as a decimal.

Accepted Answer

0.245

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 your 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\%

Test 2 Review: Step-by-Step Statistics Guidance

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