STATISTICS 2016-17
GEI
Chapters 4 & 5. Point and Interval Estimation - Exercises
1. A simple random sample of 50 items from a population with σ=6 resulted in a sample mean of
32.
a) Provide a 90% confidence interval for the population mean.
b) Provide a 95% confidence interval for the population mean.
c) Provide a 99% confidence interval for the population mean.
2. A 95% confidence interval for a population mean was reported to be 152 to 160. If σ=15, what
sample size was used in this study?
3. In an effort to estimate the mean amount spent per customer for dinner at a major Atlanta restau-
rant, data were collected for a sample of 49 customers. Assume a population standard deviation of
$5.
a) At 95% confidence, what is the margin of error?
b) If the sample mean is $24.80, what is the 95% confidence interval for the population mean?
4. The National Quality Research Center at the University of Michigan provides a quarterly measure
of consumer opinions about products and services (The Wall Street Journal, February 18, 2003). A
survey of 10 restaurants in the Fast Food/Pizza group showed a sample mean customer satisfac-
tion index of 71. Past data indicate that the population standard deviation of the index has been
relatively stable with σ=5.
a) What assumption should the researcher be willing to make if a margin of error is desired?
b) Using 95% confidence, what is the margin of error?
c) What is the margin of error if 99% confidence is desired?
5. Playbill magazine reported that the mean annual household income of its readers is $119,155 (Play-
bill, January 2006). Assume this estimate of the mean annual household income is based on a sam-
ple of 80 households, and based on past studies, the population standard deviation is known to be
σ=$ 30, 000.
a) Develop a 90% confidence interval estimate of the population mean.
b) Develop a 95% confidence interval estimate of the population mean.
c) Develop a 99% confidence interval estimate of the population mean.
d) Discuss what happens to the width of the confidence interval as the confidence level is in-
creased. Does this result seem reasonable? Explain.
6. Find the t value(s) for each of the following cases.
a) Upper tail area of 0.025 with 12 degrees of freedom
b) Lower tail area of 0.05 with 50 degrees of freedom
c) Upper tail area of 0.01 with 30 degrees of freedom
d) Where 90% of the area falls between these two t values with 25 degrees of freedom
e) Where 95% of the area falls between these two t values with 45 degrees of freedom
7. The following sample data are from a normal population: 10, 8, 12, 15, 13, 11, 6, 5.
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