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Solving Questions on Descriptive Statistics
I need help with both of these problems. I have tried everything and I can`t figure it out.
Problem Set # 6.54. A new dental bonding agent. When bonding teeth, orthodontists must maintain a dry field. A new bonding adhesive (called Smartbond) has been developed to eliminate the necessity of a dry field. However there is concern that the new bonding adhesive is not as strong as the current standard, a composite adhesive (Trends in Biomaterials & Artificial Organs, Jan. 2003). Tests on a sample of 10 extracted teeth bonded with the new adhesive resulted in a mean breaking strength (after 24 hours) of x bar = 5.07 Mpa and a standard deviation of s= .46 Mpa. Orthodontists want to know if the mean breaking strength of the new bonding adhesive is less than 5.70 Mpa, the mean breaking strength of the composite adhesive.
a. Set up the null and alternative hypotheses for the test.
b. Find the rejection region for the test using significance level=.01.
c. Compute the test statistic.
d. Give the appropriate conclusion for the test.
e. What conditions are required for the test results to be valid?
Problem Set #7.30. Performance ratings of government agencies. The U.S. Office of Management and Budget (OMB) requires government agencies to produce annual performance and accounting reports (PARS) each year. A research team at George Mason University evaluated the quality of the PARS for 24 government agencies (The Public Manager, Summer 2008), where evaluation scores ranged from 12 (lowest) to 60 (highest). The PARS file contains the 2007 and 2008 evaluation scores for all 24 agencies. (See Exercise 2.123, p.94). Data for a random sample of five of these agencies are shown in the accompanying table. Suppose you want to conduct a paired-difference test to determine whether the true mean evaluation score of government agencies in 2008 exceeds the true mean evaluation score in 2007.
Agency Score07 Score08
GSA 34 40
Agriculture 33 35
Social Security 33 33
USAID 32 42
Defense 17 32
a. Explain why the data should be analyzed using a paired-difference test.
b. Compute the difference between the 2008 score and the 2007 score for each sampled agency.
c. Find the mean and standard deviation of the differences, part b.
d. Use the summary statistics, part c, to find the test statistic.
e. Give the rejection region for the test using significance level=.10.
f. Make the appropriate conclusion in words of the problem.