Witte & Witte, 9e
Chapter 12
Page 1 of 3 Pages
Chapter 12: Estimation (Confidence Intervals)
Exercise 1
The American Wedding Study 2009 provides information related to weddings in the
United States. The results are based on a sample of 3,946 brides. Calculate the standard
error and construct a 95 percent confidence interval for the unknown population mean.
Sources:
http://honeymoons.about.com/cs/eurogen1/a/weddingstats.htm
http://press.brides.com/Bridescom/PressReleases/Article2073.htm
http://www.housewares.org/kc/gourmet/4.aspx
a. Average total amount spent on a wedding is $28,082. Assume that the population
standard deviation equals $6,000.
b. Average number of guests at a destination wedding equals 90. Assume that the
population standard deviation equals 20 guests.
c. Average age of the bride is 27 years. Assume that the population standard
deviation equals 2 years.
d. Average age of the groom is 29 years. Assume that the population standard
deviation equals 2 years.
e. The couple is engaged for an average of 14 months. Assume that the population
standard deviation equals 3 months.
f. The average amount spent on an engagement ring is $6,348. Assume that the
population standard deviation equals $1,000.
Answers:
a.
b.
c.
d.
e.
f.
Standard Error = 95.52; 95% CI: $27,894.78 - $28,269.22
Standard Error = 0.32; 95% CI: 89.37 – 90.63
Standard Error = .03; 95% CI: 26.94 – 27.06
Standard Error = .03; 95% CI: 28.94 – 29.06
Standard Error = .05; 95% CI: 13.90 – 14.10
Standard Error = 15.92; 95% CI: $6,316.80 - $6,379.20
Exercise 2
The 2006-2007 Consumer Expenditure Survey for the Baltimore Metropolitan area
provided information on average annual expenditures. Source:
http://www.bls.gov/ro3/cexbalt.pdf. Use a sample size of 100 for each of the following
problems.
a. Mean spent on food at home = $3,386. Assume that the population standard
deviation equals $700.
(1) Compute a 95% confidence interval and calculate the confidence interval
width.
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Witte & Witte, 9e
Chapter 12
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(2) Compute a 99% confidence interval and calculate the confidence interval
width.
b. Mean spent on food away from home = $2,836. Assume that the population
standard deviation equals $650.
(1) Compute a 95% confidence interval and calculate the confidence interval
width.
(2) Compute a 99% confidence interval and calculate the confidence interval
width.
c. Mean spent on entertainment = $2,726. Assume that the population standard
deviation equals $500.
(1) Compute a 95% confidence interval and calculate the confidence interval
width.
(2) Compute a 99% confidence interval and calculate the confidence interval
width.
d. Mean spent on tobacco products and smoking supplies = $229. Assume that the
population standard deviation equals $80.
(1) Compute a 95% confidence interval and calculate the confidence interval
width.
(2) Compute a 99% confidence interval and calculate the confidence interval
width.
Problem 1 Answers:
a. (1) 95% CI: $3,248.80 - $3,523.20; Width = $274.40
(2) 99% CI: $3,205.40 - $3,566.60; Width = $361.20
b. (1) 95% CI: $2,708.60 - $2,963.40; Width = $254.80
(2) 99% CI: $2,668.30 - $3,003.70; Width = $335.40
c. (1) 95% CI: $2,628.00 - $2,824.00; Width = $196.00
(2) 99% CI: $2,597.00 - $2,855.00; Width = $258.00
d. (1) 95% CI: $213.32 - $244.68; Width = $31.36
(2) 99% CI: $208.36 - $249.64; Width = $41.28
2. Look at your problem 1 results and present a summary statement regarding the
relationship between the 95% confidence interval and 99% confidence interval for the
same set of data.
Answer:
The 99% confidence interval is wider than the 95% confidence interval.
Exercise 3
A Harris poll conducted in July 2009 asked respondents to indicate the prestige they
associated with a number of different professions. The top choice was the profession of
firefighter. The results indicated that 62% of the respondents thought that the profession
of firefighter had very great prestige, with a margin of error of +/- 4% for a 95%
confidence interval. Source: http://www.pollingreport.com/work.htm
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Chapter 12
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a. Calculate the lower and upper bounds of the 95% confidence interval.
b. Calculate the confidence interval width.
c. Based on the 95% confidence interval, is it likely that the true population
proportion is equal to 50 percent? Explain your answer.
d. Based on the 95% confidence interval, is it likely that the true population
proportion is equal to 60 percent? Explain your answer.
Answers:
a. Lower bound = 58%; Upper bound = 66%
b. Confidence interval width = 66 – 58 = 8
c. No; We are 95% confident that the true proportion falls between 58% and 66%.
The suggested proportion of 50% is less than the lower bound of the confidence
interval.
d. Yes; We are 95% confident that the true proportion falls between 58% and 66%.
The suggested proportion of 60% is captured in this interval.
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