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22:22, 27/01/2026
Confidence Intervals: Estimating Means and Proportions in Statistics - Studocu Confidence Intervals
1. The temperature readings for 20 winter days in Grand Rapids, Michigan are normally
distributed with mean 5.5 degrees and a standard deviation of 1.5. Determine the 90%
confidence interval estimate for the winter mean temperature.
2. A sample of 49 measurements of tensile strength (roof hanger) are calculated to have a mean
of 2.45 and a standard deviation of 0.25. Determine the 95% confidence interval for the measurements of all hangers.
3. If we repeatedly draw samples of size 100 from the population of teenagers, 95% of the values
of sample means will be such that the population mean amount of time teenagers spend on the
internet would be somewhere between 6.206 hours and 6.794, and 5% of the values of the
sample mean will produce intervals that would not include the population mean.
a. Determine the 99% confidence interval estimate of the population mean.
b. Determine the 90% confidence interval estimate of the population mean.
c. Determine the 95% confidence interval estimate of the population mean if the sample size is changed to 300.
4. A quality control engineer is interested in the mean length of sheet insulation being cut
automatically by machine. The desired length of the insulation is 12 feet. It is known that the
standard deviation in the cutting length is 0.15 feet. A sample of 60 cut sheets yields a mean
length of 12.15 feet. This sample will be used to obtain a 99% confidence interval for the mean length cut by machine.
a. What is the critical value to use in obtaining the confidence interval?
b. Develop the 99% confidence interval for .
5. Find the sample size needed to estimate a population mean to within 2 units of the sample
mean, with a 95% confidence level, when the population standard deviation equals 8.
6. To estimate with 99% confidence the mean of a normal population, whose standard deviation
is assumed to be 6 and the maximum allowable sampling error is assumed to be 1.2, requires a random sample of what size?
7. The sample size needed to estimate a population mean to within 50 units of the sample mean
was found to be 97. The population standard deviation was 250, then what confidence level was used?
8. A statistician wants to estimate the mean weekly family expenditure on clothes. She believes
that the standard deviation of the weekly expenditure is $125. Determine with 99% confidence 22:22, 27/01/2026
Confidence Intervals: Estimating Means and Proportions in Statistics - Studocu
the number of families that must be sampled to estimate the mean weekly family expenditure on clothes to within $15. 22:22, 27/01/2026
Confidence Intervals: Estimating Means and Proportions in Statistics - Studocu
9. How large a sample of state employees should be taken if we want to estimate with 98%
confidence the mean salary to within $2000? The population standard deviation is assumed to be $10,500.
10. The owner of Britten’s egg farm wants to estimate the mean number of eggs laid per chicken.
A sample of 20 chickens shows they laid an average of 20 eggs per month with a standard
deviation of 2 eggs per month.
a) What is the value of the population mean? What is the best estimate of this value?
b) What assumption do we need to make?
c) For the 95% confidence level what is the value of the critical point?
d) Develop the 95% confidence interval for the population mean.
e) Would it be reasonable to conclude that the population mean is 21 eggs?
f) Would it be reasonable to conclude that the population mean is 25 eggs?
11. The American Sugar Producers Association wants to estimate the mean yearly sugar
consumption. A sample of 16 people reveals the mean yearly consumption to be 60 pounds with
a standard deviation of 20 pounds.
a) What is the value of the population mean?
b) What distribution do we use?
c) Find the critical point for the 90% confidence level.
d) Develop the 90% confidence interval for the population mean.
e) Would it be reasonable to conclude that the population mean is 63 pounds?
12. The union representing the Institute of Actuaries (IOA) is considering a proposal to merge
with the Faculty of Actuaries (FOA). According to the IOA union bylaws, at least three-fourths of
the union membership must approve any merger. A random sample of 2,000 current IOA
members reveals 1,600 plan to vote for the merger proposal.
a) Develop a 95% confidence interval for the population proportion
b) Basing your decision on this sample information, can you conclude that the necessary
proportion of IOA members favor the merger?
c) Explain your answer to part b). 22:22, 27/01/2026
Confidence Intervals: Estimating Means and Proportions in Statistics - Studocu
13. The owner of the Quick Fill Gas Station wished to determine the proportion of customers who
use a credit or debit card for their fuel purchase. A sample of 100 customers was surveyed and it
was found that 80 paid at the pump.
a. Estimate the value of the population proportion 22:22, 27/01/2026
Confidence Intervals: Estimating Means and Proportions in Statistics - Studocu
b. Calculate the standard error of the proportion
c. Develop a 95% confidence interval for the population proportion d. Interpret your findings
14. Foxy TV network is looking in to replacing its prime time CSI show with a family oriented
comedy show. Before a decision is made, a sample of 400 viewers are asked for their opinions.
After viewing the pilot for the comedy, 250 indicated that they would watch the show and
suggested it should replace the CSI show.
a. Estimate the value of the population proportion
b. Calculate the standard error of the proportion
c. Develop a 99% confidence interval for the population proportion d. Interpret your findings
15. Silkscreen Printing Inc., purchases coffee mugs on which to print funny logos. A large
shipment was received and the owner wants to ensure that the quality is good and that they are
not defective. A sample of 300 cups was chosen at random and it was found that 15 were defective.
a. Estimate the value of the population proportion
b. Develop a 95% confidence interval for the proportion defective
c. The owner of Silkscreen Printing Inc., has an agreement with the supplier, that if 10% or
more of the shipment is defective, he may return it. Should he return this shipment? 22:22, 27/01/2026
Confidence Intervals: Estimating Means and Proportions in Statistics - Studocu 22:22, 27/01/2026
Confidence Intervals: Estimating Means and Proportions in Statistics - Studocu