STATS Final Examination Questions Set

Page 1

Question 1. 1.(TCO A)
Consider the following age data, which is the result of selecting a
random sample of 22 Boeing 747 airplanes that are owned by United Airlines.
The age of each airplane is given in years.

17
5
5
12
8
5
8
16
14 12
22
15
5
8
17
5
4
2
22
17 20
23

a. Compute the mean, median, mode, and standard
deviation, Q1, Q3, Min, and Max for the above
sample data on age of Boeing 747 airplanes owned by United Airlines.
b. In the context of this situation, interpret the Median, Q1,
and Q3. (Points : 33)

Question 2. 2.(TCO B) Consider the following
data on new customers for AJ Auto Insurance, specifically the information
of the risk level of the customer and the number of tickets they have had
in the last year.

0

1

2 or more

Total

Low Risk

56

22

8

86

Medium Risk

18

40

12

70

High Risk

11

13

20

44

Total

85

75

40

200

If you choose a customer at random, then find the probability that the
customer is

a. low risk.
b. low risk and had two or more tickets in the last year.
c. medium risk, given that the customer had zero tickets in the last year.
(Points : 18)

Question 3. 3.(TCO B)According to a
survey by the Opinion Research Corporation, 60% of all clerical workers in
the United States “liked their jobs very much.” A random sample of 15
clerical workers is selected. Find the probability that

a. exactly nine of these clerical workers “liked their jobs very much.”
P(X=9) = 15C9*0.6^9*0.4^6 = 0.2066
b. at least seven of these clerical workers “liked their jobs very much.”
c. fewer than five of these clerical workers “liked
their jobs very much.” (Points : 18)P

Question 4. 4.(TCO B) A study of homeowners in
the 5th congressional district in Maryland found that their annual
household incomes are normally distributed with a mean of $41,182 and a
standard deviation of $11,990 (based on data from Nielsen Media Research).

a. What percentage of household incomes are greater than $30,000?

b. What percentage of household incomes are between $25,000 and $40,000?

c. If an advertising campaign is to be targeted at those whose household
incomes are in the top 20%, find the minimum income level for this target
group? (Points : 18)

Question 5. 5.(TCO C) The Ford Motor Company
wishes to estimate the mean dollar amount of damage done to a Ford Explorer
as a result of a 10 mph crash into the rear bumper of a parked car. The
sample results are as follows.

Sample Size = 36
Sample Mean = $638
Sample Standard Deviation = $115

a. Construct a 95% confidence interval for the average dollar amount of
damage.
b. Interpret this interval.
c. How large a sample size will need to be selected if
we wish to have a 95% confidence interval for the average dollar amount of
damage with a margin for error of $10? (Points : 18)

Question 6. 6.(TCO C) A clock company is
concerned about errors in assembly of their custom made clocks. A random
sample of 120 clocks from today’s production yields nine clocks with
assembly errors.

a. Compute the 95% confidence interval for the percentage of clocks with
assembly errors in today’s production.

b. Interpret this confidence interval.
c. How many clocks should be selected in order to be 95%
confident of being within 2% of the population percentage of clocks with
assembly errors in today’s production? (Points : 18)

Question 7. 7.(TCO D) According to Information
Resources Inc., based on sales of teeth-cleaning products, Crest toothpaste
controlled a 31.2% share of the market. A researcher from a rival company
believes that this figure is high, and that in fact, Crest controls less
than 31.2% of the market. A simple random sample of 400 consumers yields
116 use Crest. Does the sample data provide evidence to conclude that the
researcher from the rival company is correct (witha
= .05)? Use the hypothesis testing procedure outlined below.

a. Formulate the null and alternative hypotheses.

b. State the level of significance.

c. Find the critical value (or values), and clearly show the rejection and
nonrejection regions.

d. Compute the test statistic.

e. Decide whether you can reject Ho and accept Ha or not.
f. Explain and interpret your conclusion in part
e. What does this mean?
g. Determine the observed p-value for the hypothesis
test and interpret this value. What does this mean?

h. Does the sample data provide evidence to conclude that Crest’s market
share is below 31.2% (witha = .05)? (Points : 24)

Question 8. 8.(TCO D) A new car dealer
calculates that the dealership must average more than 4.5% profit on sales
of new cars. A random sample of 81 cars gives the following result.

Sample Size = 81
Sample Mean = 4.97%
Sample Standard Deviation = 1.8%

Does the sample data provide evidence to conclude that the dealership
averages more than 4.5% profit on sales of new cars (usinga
= .10)? Use the hypothesis testing procedure outlined below.

a. Formulate the null and alternative hypotheses.

b. State the level of significance.
c. Find the critical value (or values), and clearly show
the rejection and nonrejection regions.
d. Compute the test statistic.
e. Decide whether you can reject Ho and accept Ha or
not.

f. Explain and interpret your conclusion in part e. What does this mean?
g. Determine the observed p-value for the hypothesis
test and interpret this value. What does this mean?

h. Does the sample data provide evidence to conclude
that the dealership averages more than 4.5% profit on sales of new cars
(usinga = .10)? (Points : 24)