# MATHEMATICS

1.The MPG (miles per gallon) for a certain compact car is normally distributed with a mean of 31 and a standard deviation of 0.8. What is the probability that the MPG for a randomly selected compact car would be less than 32?

0.5596

0.3944

0.8944

0.1056

2.In a simple regression, there are n – 2 degrees of freedom associated with the error sum of squares (SSE).

True

False

3.A researcher’s results are shown below using Femlab (labor force participation rate among females) to try to predict Cancer (death rate per 100,000 population due to cancer) in the 50 U.S. states.

Source of variation df SS MS F

Regression 1 5377.836 5377.836 5.228879

Residual 48 49367.389 1028.487

Total 49 54745.225

What is the R2 for this regression?

.1605

.0982

.9018

.8395

[The following information applies to the questions displayed below.]

The sodium content of a popular sports drink is listed as 204 mg in a 32-oz bottle. Analysis of 14 bottles indicates a sample mean of 210.5 mg with a sample standard deviation of 24.2 mg.

4.(a)

State the hypotheses for a two-tailed test of the claimed sodium content.

H0: µ ≤ 204 vs. H1: µ > 204

H0: µ = 204 vs. H1: µ ≠ 204

H0: µ ≥ 204 vs. H1: µ < 204

5.

(b)

Calculate the t test statistic to test the manufacturer’s claim. (Round your answer to 4 decimal places.)

Test statistic

6.

(c)

At the 1 percent level of significance (α = 0.01) does the sample contradict the manufacturer’s claim?

H0. The sample

the manufacturer’s claim.

7.

(d-1)

Use Excel to find the p-value and compare it to the level of significance. (Round your answer to 4 decimal places.)

The p-value is . It is

than the significance level 0.01.

(d-2) Did you come to the same conclusion as you did in part (c)?

Yes

No

8.A charity raffle prize is $1,000. The charity sells 4,000 raffle tickets. One winner will be selected at random. At what ticket price would a ticket buyer expect to break even?

$0.25

$0.50

$0.75

$1.00

9.At Joe’s Restaurant, 80 percent of the diners are new customers (N), while 20 percent are returning customers (R). Fifty percent of the new customers pay by credit card, compared with 70 percent of the regular customers. If a customer pays by credit card, what is the probability that the customer is a new customer?

.7407

.5000

.5400

.8000

10.Within a given population, 22 percent of the people are smokers, 57 percent of the people are males, and 12 percent are males who smoke. If a person is chosen at random from the population, what is the probability that the selected person is either a male or a smoker?

.67

.22

.43

.79