1.A package of light bulbs promises an average life of more than 750 hours per bulb. A consumer group did not believe the claim and tested a sample of 40 bulbs. The average lifetime of these 40 bulbs was 740 hours with hours. The manufacturer responded that its claim was based on testing hundreds of bulbs.

a.If the consumer group and manufacturer both make 95% confidence intervals for the population's average lifetime, whose will probably be shorter?

Can you tell for certain?

b.Given the usual sampling assumptions, is there a 95% probability that 750 lies in the 95% confidence interval of the manufacturer?

c.Is the manufacturer's confidence interval more likely to contain the population mean because it is based on a larger sample?

2.The following random sample was selected from a normal distribution: 4,6,3,5,9,3.

a.Construct a 90% confidence interval for the population mean .

90% confidence interval is (_______________,_______________)

b.Construct a 95% confidence interval for the population mean .

95% confidence interval is (_______________,_______________)

c.Construct a 99% confidence interval for the population mean .

99% confidence interval is (_______________,_______________)

d.Assume that the sample mean and sample standard deviation remain exactly the same as those you just calculated but are based on a sample of n=26 observations rather than n=6 observations. Repeat parts a-c.

a)

90% confidence interval is (_______________,_______________)

b)

95% confidence interval is (_______________,_______________)

c)

99% confidence interval is (_______________,_______________)

e.What is the effect of increasing the sample size on the width of the confidence intervals?

3.IOP create billions of dollars of new wealth for owners, managers, and employees of companies that were previously privately owned. Nevertheless, hundreds of large and thousands of small companies remain privately owned. The revenues of a random sample of 15 firms from Forbes 441 Largest Private Companies list is given in the table below:

COMPANY

REVENUE

Enterprise

13.1

FlyingJ

14.32

Tenaska

11.6

Wawa

5.05

Ergon

4.49

Brookshire

2.2

BrightStar

3.66

Bose

2.18

MaryKay

2.4

LLBean

1.62

RoomToGo

1.75

SAS

2.15

BlueTee

1.1

Printpack

1.36

USOil

2.19

a.Describe the population from which the random sample was drawn.

b.Use a 98% confidence interval to estimate the mean revenue of the population of companies in questions.

98% confidence interval is (_______________,_______________)

c.Interpret your confidence interval in the context of the problem.

d.What characteristic must the population possess to ensure the appropriateness of the estimation procedure used in part b.

e.Suppose Forbes reports that the true mean revenue of the 441 companies on the list is $5.0 billion. Is the claim believable?