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e. Is the assumption that the underlying population of measurements is normally

distributed necessary to ensure the validity of the confidence intervals in parts a-d?

2

ECON 15B

3. 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 s = 30 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?

3

ECON 15B

2. A random sample of n measurements was selected from a population with unknown mean u

and known standard deviation o. Calculate a 95% confidence interval for u for each of the

following situations:

a. n = 75, 7 = 28,02 = 12

b. n = 200, x = 102,02 = 22

c. n = 100,X = 15,0 = .3

d. n = 100, X = 4.05,0 = .83

e. Is the assumption that the underlying population of measurements is normally

distributed necessary to ensure the validity of the confidence intervals in parts a-d?

2

ECON 15B

3. 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 s = 30 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?

ECON 15B

Homework 3

1. Budget lapsing occurs when unspent funds do not carry over from one budgeting period to the

next. Because budget lapsing often leads to a spike in expenditures at the end of the fiscal year,

the researchers recorded expenses per full-time equivalent employee for each in a sample of

1,751 army hospitals. The sample yielded the following summary statistics: # = $6,563 and s =

$2,484. Estimate the mean expenses for full-time equivalent employee of all U.S. army hospitals

using a 90% confidence interval. Interpret the result.

1

ECON 15B

2. A random sample of n measurements was selected from a population with unknown mean u

and known standard deviation o. Calculate a 95% confidence interval for u for each of the

following situations:

a. n = 75, 7 = 28,02 = 12

b

n = 200 ? = 102,2 = 22

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Explanation & Answer:

4 Questions

Tags:

standard deviation

confidence interval

Lower Limit

Upper limit

budget lapsing

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