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Confidence interval for mean

1. In a study of the income of U.S factory workers, a random sample of 125 workers shows a sample mean of $29,000. Assume that the population standard deviation is $4,500.

A) Compute the 90%, 95%, and 99% confidence intervals for the unknown population mean.
B) Briefly discuss what happens to the width of the confidence interval estimate as the confidence level increases. Does this seem reasonable?

2. In a study of the starting salary of college graduates with degrees in Accounting, a random sample of 28 graduates shows a sample mean of $35,000 and a sample standard deviation of $2,900.

A) Compute and explain a 95% confidence interval estimate of the unknown population mean starting salary for Accounting graduates.
B) What is the essential difference between this problem and problem #1?

3. A telephone poll of 700 American adults asked "Where would you rather go in your spare time?" One response, by 250 adults, was "a casino". Compute and explain a 95% confidence interval estimate of the proportion of all American adults who would respond "a casino".

Solution Preview

Please see the attached file for proper format of tables.

PROBABILITY

1. In a study of the income of U.S factory workers, a random sample of 125 workers shows a sample mean of $29,000. Assume that the population standard deviation is $4,500.

a. Compute the 90%, 95%, and 99% confidence intervals for the unknown population mean.
The confidence interval is given by . Since the population variance is known, Normal distribution is used for the computation of the confidence interval.

Details
Confidence Interval Estimate for the Mean

Data
Population Standard Deviation 4500
Sample Mean 29000
Sample Size 125
Confidence Level 90%

Intermediate Calculations
Standard Error of the Mean 402.4922359
Z Value -1.64485363
Interval Half Width 662.0408141

Confidence Interval
Interval Lower Limit 28337.95919
Interval Upper Limit 29662.04081

Confidence Interval Estimate for the Mean

Data
Population Standard ...

$2.19