**Due date**: Nov. 4, 2014.

**Note**: all hypothesis testing problems should specify the null and alternative hypotheses
and report the p-value of the data.

- A large corporation has a plant that has started a pilot program to give stock options for
its assembly line workers as part of their benefits package. The corporation would like to determine
if the mean quality score for this plant exceeds the current average quality measure of 75. A
random sample of 20 production units is selected from this plant and the quality scores for these
units are obtained. The mean score for these units is 78.2 with a s.d. of 10.3.
- Does this plant have a higher mean score at the 5% level of significance?
- What is the probability this test will reject the null hypothesis if the population mean score is 80?
- Construct a 90% confidence interval for the mean score of this plant.
- Use this data as a preliminary sample to determine the sample size required to estimate the mean quality score under this program to within 2.0 with 95% confidence.

- A company is said to be out of compliance if more than 10% of all invoices contain errors,
and it is considered to be seriously out of compliance if more than 15% of all invoices contain
errors. Suppose an auditor randomly selects a sample of 1250 invoices and found that 200 contained
errors.
- Construct a 95% confidence interval for this company's error rate.
- How should the company be rated if statements about being out of compliance require 5% level of significance?
- What is the probability a company would be rated as seriously out of compliance by this test if 18% of all invoices at that company contain errors?
- What sample size should the auditor use to estimate the error rate to within 2% with 99% confidence if it is assumed that the error rate will be no more than 20%?
- Suppose the 200 erroneous invoices can be treated as a random sample from the population of
all erroneous invoices. The error amounts are contained in the file

http://www.UTDallas.edu/~ammann/stat3355scripts/Invoice.txt

Construct a 95% confidence interval for the mean error amount. Also obtain and interpret a quantile-quantile plot of these invoices compared to the normal distribution.

- A random sample of 48 students took an SAT preparation course prior to taking the SAT. The
sample mean of their quantitative SAT scores was 560 with a s.d. of 80, and the sample mean of
their verbal SAT scores was 520 with a s.d. of 110.
- Construct 95% confidence intervals for the mean quantitative SAT and the mean verbal SAT scores of all students who take this course.
- What sample size would be needed to estimate the mean verbal SAT score with 95% confidence and with error of no more than 15 if it is assumed that the s.d. is no more than 120?
- Suppose the mean scores for all students who took the SAT at that time was 525 for the quantitative and 500 for the verbal? Do the means for students who take this course differ from the means for all students at the 10% level of significance?

- A fabrication plant has just completed a contract to supply memory chips to a computer
manufacturer that requires the defective rate of these chips to be no more than 8%. The plant has
just installed new equipment to produce these chips. An initial production run of 400 chips will be
obtained and one of three actions will be taken depending on the results of this run. If it is shown
that more than 8% of the chips are defective, then the equipment will be recalibrated to reduce the
defective rate; if it is shown that less than 8% of chips are defective, then cheaper raw material
will be used to reduce costs; otherwise, the equipment will be unchanged and production will begin.
Suppose that among the initial production of 400 chips it was found that 28 chips were defective.
- What action should plant management take at the 5% level of significance?
- What is the probability that the null hypothesis would be rejected if the population defective rate is actually 10%?
- Estimate the current defective rate with a 95% confidence interval.
- In the future plant management would like to estimate the defective rate to within 1% using 95% confidence intervals. What sample size would be required to accomplish this if it is assumed that the defective rate would be no more than 10%?

- A large corporation would like to determine if employee job satisfaction will improve if it
includes profit sharing based on quality scores for its factory workers. To answer this question,
a pilot program was begun at one of its factories. A random sample of 30 workers from this factory
was selected and, separately, a random sample of 30 workers was selected from another of its
factories that did not implement this program. Prior to the start of the program each worker in
these samples was given a test of job satisfaction as part of their normal review process. This test
was then administered to the same employees six months after the start of the new program. Use 5%
level of significance for the following questions. The data is contained in the file

http://www.UTDallas.edu/~ammann/stat3355scripts/Pilot.csv

- Is there a difference between the mean satisfaction scores of these two factories before the pilot program is started?
- Let
*SatisImprov*be defined as*SatisImprov = After - Before*.

Is there a difference between the means of*SatisImprov*at these factories? - Construct a 95% confidence interval for
*SatisImprov*at the pilot factory.

- A soft drink company would like to increase its market share of diet soft drinks among 18-25
year old females with a new ad campaign targeting this population by placing ads at web sites these
women are likely to visit. A random sample of 250 females in this age bracket who drink these
products is selected to participate in a study to estimate the proportion of such women who visit
these sites, as well as how often they visit them in a week. The file

http://www.UTDallas.edu/~ammann/stat3355scripts/Diet.txt

contains the number of times each woman in this sample visited the sites during a typical week.- Construct a 95% confidence interval for the proportion of such women who visit those sites at least once a week.
- What sample size would be required to estimate the proportion of such women who visit these sites at least once a week to within 2% with 95% confidence if the company makes no prior assumptions about the population proportion?
- Now use those women who visited the sites at least once a week as a random sample of all such women and construct a 95% confidence interval for the mean number of visits during a week.

2014-10-21