ECO 320
Mathematical Statistics
ECO 320: Mathematical Statistics
Week 12: Additional Exercises
Samuele Centorrino1
Problem 1
Data released by the National Center for Health Statistics showed that the mean age at which women had their first child
was 25.0 in 2006 (The Wall Street Journal, February 4, 2009). The reporter noted that this was the first decrease in the
average age at which women had their first child in several years. A recent sample of 42 women has been collected
concerning the age at which these women had their first child. The sample mean is X̄ = 24.05 and the sample variance
is s2 = 34.63. Do the data indicate a change from 2006 in the mean age at which women had their first child? Use
α = .05.
Problem 2
The chamber of commerce of a Florida Gulf Coast community advertises that area residential property is available at a
mean cost of $125,000 or less per lot. Suppose a sample of 32 properties provided a sample mean of $130,000 per lot
and a sample standard deviation of $12,500. Use a .05 level of significance to test the validity of the advertising claim.
Problem 3
The daily car rental rates for a sample of eight cities follow.
City
Daily Car Rental Rate($)
Atlanta
47
Chicago
50
Dallas
53
New Orleans
45
Phoenix
40
Pittsburgh
43
San Francisco
39
Seattle
37
1) Compute the sample variance and the sample standard deviation for these data.
2) A car agency states that the variance is not higher than 28. How would you test this claim at the significance level
α = 0.01?
1 Please email me at samuele.centorrino@stonybrook.edu if you find any typo or mistake.
©2018 Samuele Centorrino. All rights reserved.
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ECO 320
Mathematical Statistics
3) The National Association of Rental car Agencies states that the variance is equal to 12. How would you test this
claim at the significance level α = 0.05?
Problem 4
Shorney Construction Company bids on projects assuming that the mean idle time per worker is 72 or fewer minutes
per day. A sample of 30 construction workers will be used to test this assumption. Assume that the population standard
deviation is 20 minutes. Use α = 0.05.
1) State the hypotheses to be tested.
2) What is the probability of making a Type II error when the population mean idle time is 80 minutes?
3) What is the probability of making a Type II error when the population mean idle time is 75 minutes?
4) What is the probability of making a Type II error when the population mean idle time is 73 minutes?
5) Define the power of a test. How would you say that the power of this test changes as the population mean satisfies
the null hypothesis?
©2018 Samuele Centorrino. All rights reserved.
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