______

NAME

For this test assume  = .05

unless otherwise stated.

MSIS 361A

FALL, 2000
JOHN LAWRENCE

EXAM#2

You may, but do not have to,

use Excel for problem 1. If you

do, precisely label the part and

work on worksheet Problem 1.

The others require Excel.

Theory/Concepts

1.(51)______

Applications

2.(9)______

3.(9)______

4.(9)______

5.(9)______

6.(9)______

7.(9)______

TOTAL(105)______

A SCORE OF 100 WILL BE CONSIDERED PERFECT!

1. Cox Communications in Orange County is currently pushing their digital television service that requires the installation of special cable boxes on each television set. Because of the limited amount of cable boxes, Cox is currently limiting the number of sets per Cox household that can have the digital service.

Last year Cox determined that the average number of televisions in Cox households was 2.28 and the standard deviation of the number of televisions in Cox households was .45.

Barry Johnson, who works for Cox Communications, was asked to perform a study to determine the average number of televisions in households serviced by Cox Communications this year. He randomly surveyed 750 Cox customers and determined that between them, there were a total of 1740 televisions. He stated that simply because 1740/750 = 2.32, this was conclusive proof that the number of televisions per household has increased.

a.Briefly state why, without any further statistical analysis, Barry's assertion, as it stands is not valid.

b.Was Barry lucky? That is, can you conclude that the average number of televisions per Cox household has increased from last year's value of 2.28? (Assume the standard deviation has not changed.) because

Show work below.


By hand: Check this box if you used EXCEL.

c.What is the p-value for this test?

Show work below. Check this box if you used EXCEL.

P(Z>2.43) = .5-.4925 = .0075

What does this mean?

d.Did you have to assume that the distribution of the number of television sets in Cox households had a normal distribution to perform the analysis in part b?

because

e.For this problem, what is the definition of the random variable X?

What is its distribution? What is its standard deviation?

f.For this problem, what is the definition of the random variable ?

What is its distribution? What is its standard deviation?

g.To do part b, you assume that  = .05. Explain briefly what that means in the context of this problem.

h.Give a 95% confidence interval for the average number of televisions in Cox households.

Show work below. Check this box if you used EXCEL.

i.What do we mean by a 95% confidence interval for this problem?

j.Give an 85% confidence interval for the average number of televisions in Cox households.

Show work below. Check this box if you used EXCEL.

By hand:


k.Suppose the true mean number of televisions in Cox households was actually 2.30. What would have been the probability that you would have gotten a sample that would not allow you to conclude that the average was greater than 2.28?

What do we call this probability?

Would this value have been greater or smaller if the true mean were actually 2.40?

Show work below. Check this box if you used EXCEL.

1. Reject H0 if

2. If  = 2.30,

 =

l.Suppose the true mean number of television sets in Cox households was actually 2.30. What is the probability that a Cox household has 3 or more sets? HINT: CAREFUL!

Show work below.Check this box if you used EXCEL.

m.Suppose the true mean number of television sets in Cox households was actually 2.30. What is the probability that the average of a sample of 81 Cox household is more than 2.36 sets?

Show work below. Check this box if you used EXCEL.


n.Suppose you could assume that the number of televisions in Cox households is distributed normally and you did not have access to the fact that last year the standard deviation was .45 -- this means you have no idea of what the standard deviation truly is. You take your own survey of 5 randomly selected households and get: 2, 2, 3, 4, 1. BY HAND -- give a 95% confidence interval for the average number of television sets. Leave in " form".


HAND CALCULATIONS ON NEXT PAGE:


Problems 2-7 refer to data on the given Excel worksheets. Do all work on the worksheets and fill in the answers below. Assume all data comes from "relatively normal" distributions.

2.From the random sample shown on worksheet Problem 2, can you conclude that the average electric bill for residential customers in Mission Viejo in July > $150?

3.From the random sample shown on worksheet Problem 3, give a 99% confidence interval for average amount spent by teenagers in Orange County each month on CD's.

4.Last year the average driving time from the Fullerton campus to the Mission Viejo campus was 40 minutes with a standard deviation of 6 minutes. Assuming that the standard deviation has not changed, from the random sample shown on worksheet Problem 4, can you conclude the average driving time has changed from last year?

5.From the random sample shown on worksheet Problem 5, can you conclude that the average time spent waiting in the drive-thru line at the Jack-In-The-Box on the corner of Avery and the 5 Freeway is less than 3 minutes?

6.From the random sample shown on worksheet Problem 6, assuming that the standard deviation is 9 yards, give a 95% confidence interval for the average distance Tiger Woods drives a golf ball.

7.From the random sample shown on worksheet Problem 7, assuming a standard deviation of $.05 per gallon, can you conclude that the average price for regular unleaded gasoline in Orange County on October 20 was greater than $1.70?