1. You’re at a clearance sale at your favorite clothing store and you’re digging through a box of

discounted items. The box contains 5 sweatshirts, 6 pairs of shorts, 9 tee shirts, 2 turtleneck

sweaters, and 8 tank tops. Answer the following questions (a-d) with this information. Report

all your answers in decimal format and use four (4) decimal places. (Start each question

with the original 30 total clothing items).

a. What is the probability that you will randomly select a turtleneck sweater out of the box?

(1 point)

b. What is the probability that you will randomly select a tee shirt or a pair of shorts out of

the box?

(1 point)

C. What is the probability that you will randomly pick a sweatshirt followed by a tank top

out of the box (with replacement)?

(1 point)

d. What is the probability that you will randomly pick a sweatshirt and afterwards pick

another sweatshirt out of the box (without replacement)?

(1 point)

2. A radio producer wants to know about the relationship between listening to National Public

Radio (NPR) and college graduation. He sampled 90 people in his city and asked two

questions. One question was “Are you a college graduate (yes/no)?” The other question

asked was, “Do you listen to NPR (yes/no)?” The data are summarized below. Use this data

to answer the following questions (a-c). Report all your answers in decimal form and use

four (4) decimal places.

ve Listens to NPR

Doesn’t listen to NPR

College Graduate

60

30

Non-College Graduate

30

60

a. What is the probability that a randomly selected citizen listens to NPR?

(1 point)

b. What is the probability that a randomly selected citizen listens to NPR given that they are

a college graduate?

(1 point)

c. What is the probability that a randomly selected citizen does not listen to NPR and is a

non-college graduate?

(1 point)

2

3. The population mean number of naps taken per month by the average adult is 3 with a

population standard deviation of 1.3. Your stats professor says that she takes 5 naps per

month. Use an alpha level of 0.05 to determine whether your professor takes significantly

more naps per month than the average adult.

a.

(2

State the null and alternative hypotheses in symbols.

points)

· b. Set up the criteria for making a decision. That is, find the critical value(s).

(1 point)

c. Compute the appropriate test statistic. Show your work.

(3 points)

d.

Based on your answers above, evaluate the null hypothesis.

(1 point)

Reject

Fail to reject

(circle one)

e. State your conclusion in words.

(1 point)

f. Given your decision, what type of error could have been committed?

(1 point)

Type I error

Type II error

(circle one)

5. A researcher wants to know if there is a difference in amount of orange juice drank between

Floridians and Ohioans. He gathers a sample of Floridians and a sample of Ohioans and

experiment is provided below. Use this data and

an alpha of .05 to decide if there is a

of orange juice they drink per week. The data collected from this

difference in orange juice consumption between Floridians and Ohioans.

records how many cups

ă

s2

Ohioans

2

1.1

26

Floridians

4.5

2.2

26

1

n

(2 points)

a. State the null and alternative hypotheses in symbols.

b. Set up the criteria for making a decision. That is, find the critical value(s).

(1 point)

(3 points)

c. Compute the appropriate test statistic. Show your work.

Complete by NOT Pooling the Variance!

(1 point)

d. Based on your results, evaluate the null hypothesis. (circle one)

Reject

Fail to Reject

(1 point)

e. State your conclusion in words

(2 points)

f. Compute the 99% confidence interval.

(1 point)

g. Interpret (in words) the confidence interval you calculated above

5

4. You hear on the news that the average person consumes a population mean of 29 pounds of

cheese per year. A random sample of 25 students at Ohio University was found to consume a

sample mean of 26 pounds of cheese per year with a sample standard deviation of 4.4

year as compared to average person? (a= .01)

pounds. Do Ohio University students differ in the number of pounds of cheese consumed per

(1 point)

a.

State the null and alternative hypotheses in symbols.

b. Set up the criteria for making a decision. That is, find the critical value(s).

(1 point)

c. Compute the appropriate test statistic. Show your work.

(3 points)

d. Based on your answers above, evaluate the null hypothesis.

(1 point)

REJECT

FAIL TO REJECT (circle one)

e. State your conclusion in words.

(1 point)

f. Compute the 99% confidence interval.

(2 points)

g. In words, interpret the confidence interval you calculated above.

(1 point)

Multiple Choice

(1 point each)

6. Given a research experiment with alpha = 0.01 and beta = 0.60, what is the probability of

committing a Type II error given that the null hypothesis is incorrect in reality?

A.).99

B.).60

C.).40

D.).01

E.).00

7. The independent t-test requires the following assumption(s):

A.) Normality of distributions

B.) Heterogeneity of variance

C.) Sample size more than 30

D.) Both answers A and C

E.) All answers A and B and C

8. Which of the following is an example of conditional probability?

A.) The probability Mariah owns a cow

B.) The probability that Mariah owns a cow given that she is a farmer

C.) The probability that Mariah is a farmer

D.) The probability that Mariah owns a cow and that she is a farmer

I

9. Assuming all other factors remain constant, during hypothesis testing, if we increase our

alpha from .01 to .05, we will make it difficult to reject the null hypothesis but

our probability of making a type 1 error.

A.) More; decrease

B.) Less; increase

C.) More; increase

D.) Less; decrease

10. In your own words, what is sampling error? In other words, if we say a difference is due to

sampling error, what are we saying?

6

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