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# MAT222-2006Fall - M AT 2 22 F inal December 1 3 2 006 N ame...

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MAT 222 Final (December 13, 2006) Name: _ *************** 1. There are 7 problems and a total of 9 pages in this booklet. 2. Show all of your work and label your answers clearly. 3. If you use a table, state the table used: for example 1.887 (from Table A). 4. If you use a function on the TI 83 (or TI 89), write out the command you entered as well as the result: for example, 0.0668 (normalcdf (-10, -1.5, 0.1)). *************** 1 2 3 4 5 6 7 !Total! __ 1

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1. (19 pts) A researcher wished to compare the average amount of time spent in extracurricular activities by high school students in a suburban school district with that in a school district of a large city. The researcher obtained a simple random sample of 50 high school students in a large suburban school district and found the mean time spent in extracurricular activities per week to be 6 hours with a standard deviation of 3 hours. The researcher also obtained an independent simple random sample of 30 high school students in a large city school district and found the mean time spent in extracurricular activities per week to be 4 hours with a standard deviation of 2 hours. Is the difference between the mean time spent for extracurricular activities in the two districts significant? Let JLl and JL2 represent the mean amount of time spent in extracurricular activities per week by the populations of all high school students in the suburban and city school districts, respectively. Assume that the population standard deviations are not equal and that two sample t procedures are safe to use. (a) Answer the question by finding a 95% confidence interval for ~q - JL2 .. (b) Answer the question by carrying out a test at the 5% level of signicance. Be sure to state your hypotheses, test statistic with degrees of freedom, and the P-value. 2
2. (18 pts) After once again losing a football game to the college's arch rival, the alumni associ- ation conducted a survey to see if alumni were in favor of firing the coach. A simple random sample of 100 alumni from the population of all living alumni was taken. Sixty-four of the alumni in the sample were in favor of firing the coach. Let p represent the proportion of all living alumni who favor firing the coach. (a) What is a 99% confidence interval for p? (b) Suppose the alumni association wished to see if the majority of alumni are in favor of firing the coach. To do this they test the hypotheses Ho : p = 0.50 versus H a : p > 0.50. What is the P-value for this hypothesis test? Draw your conclusion at the 5% level of significance. 3

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3. (13 pts) Are avid readers more likely to wear glasses than those who read less frequently? Three hundred men in New York were selected at random and characterized as to whether they wore glasses and whether the amount of reading they did was above average, average, or below average. The results are presented in the following table.
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