1. A random sample is drawn from a population of known standard deviation 22.1. Construct a 95% confidence interval for the population mean based on the information given (not all of the information given need be used).
a. n = 121, x-=82.4, s = 21.9
b. n = 81, x-=82.4, s = 21.9
2. A random sample is drawn from a population of unknown standard deviation. Construct a 98% confidence interval for the population mean based on the information given.
a. n = 225, x-=92.0, s = 8.4
b. n = 64, x-=92.0, s = 8.4
3. A random sample of size 256 is drawn from a population whose distribution, mean, and standard deviation are all unknown. The summary statistics are x-=1011 and s = 34.
a. Construct a 90% confidence interval for the population mean μ.
b. Construct a 99% confidence interval for the population mean μ.
c. Comment on why one interval is longer than the other.
4. Four hundred randomly selected working adults in a certain state, including those who worked at home, were asked the distance from their home to their workplace. The average distance was 8.84 miles with standard deviation 2.70 miles. Construct a 99% confidence interval for the mean distance from home to work for all residents of this state.
5. A corporation monitors time spent by office workers browsing the web on their computers instead of working. In a sample of computer records of 50 workers, the average amount of time spent browsing in an eight-hour work day was 27.8 minutes with standard deviation 8.2 minutes. Construct a 99.5% confidence interval for the mean time spent by all office workers in browsing the web in an eight-hour day.
6. A power wrench used on an assembly line applies a precise, preset amount of torque; the torque applied has standard deviation 0.73 foot-pound at every torque setting. To check that the wrench isoperating within specifications it is used to tighten 100 fasteners. The mean torque applied is 36.95 foot-pounds with sample standard deviation 0.62 foot-pound. Construct a 99.9% confidence interval for the mean amount of torque applied by the wrench at this setting. Hint: Not all the information provided is needed.
7. For each of 40 high school students in one county the number of days absent from school in the previous year were counted, with the results shown in the frequency table.
x| 012345
f| 24 7 5 2 1 1
8. Large Data Set 1 records the GPAs of 1,000 college students. Regarding it as a random sample of all college students, use it to construct a 95% confidence interval for the mean GPA of all students.
https://www.flatworldknowledge.com/sites/all/files/data1.xls
9. Large Data Set 1 lists the GPAs of 1,000 students.
https://www.flatworldknowledge.com/sites/all/files/data1.xls
a. Regard the data as arising from a census of all freshman at a small college at the end of their first academic year of college study, in which the GPA of every such person was measured. Compute the population mean μ.
b. Regard the first 36 students as a random sample and use it to construct a 95% confidence for the mean μ of all 1,000 GPAs. Does it actually capture the mean μ?