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final exam solutions - ECON 2300 CUMULATIVE FINAL EXAM...

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ECON 2300 – CUMULATIVE FINAL EXAM SOLUTIONS FALL SEMESTER, 2009 1. A consumer products manufacturer wants to estimate the mean water absorbency of its new brand of paper towels. For a random sample of 64 paper towels, the mean water absorbency was 450 grams. Assume the population standard deviation is σ = 21 grams. (Assume the water absorbency rate is normally distributed.) a. Compute and interpret a 99% confidence interval estimate for the mean water absorbency of its new brand of paper towels. x σ = n = 21/√64 = 2.625 grams Z .01/2 = 2.576 99% confidence interval estimate of the mean water absorbency = [450 +/- 2.576 * 2.625] =[450-6.762; 450+6.762] = [443.2 grams; 456.8 grams] It is estimated, with 99% confidence, that the mean water absorbency rate for the new paper towels is 443.2 to 456.8 grams. b. Explain how you determined whether to use a z-statistic or a t-statistic to develop your confidence interval estimate. Because we know the population standard deviation, σ = 21 grams, we use a z statistic. c. Suppose you want to estimate the mean water absorbency of the new paper towels to within 5 grams (maximum margin of error). Use a 99% confidence level and compute the necessary sample size. n = (z α /2 * σ ) / E ) 2 or (2.576 * 21) / 5 ) 2 = 117.1 or 118 paper towels 2. A car dealer currently bases its labor charge for a tire rotation and alignment job on its belief that the mean time spent on such a job is 40 minutes. For a random sample of 36 tire rotation and alignment jobs performed at the dealership, the mean time spent on the jobs was 46 minutes with a standard deviation of 15 minutes. Does that sample data provide evidence that the mean time needed to rotate and align a set of tires is greater (> 40) than 40 minutes? Use a significance level of α = .10 in addressing that question. a. Define the null and alternative hypotheses below. Ho: μ < 40 minutes Ha: μ > 40 minutes
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ECON 2300 – CUMULATIVE FINAL EXAM – FALL, 2009 (online) SOLUTIONS pg. 2 b. State the decision / rejection rule for this test. Because we do not know the population standard deviation, we must use a critical t- value. Critical t .10,35 = 1.69 Decision rule: Do not reject Ho if computed t < t .10,35 = 1.69 μ=40 =46 0 t .10,35 = 1.69 2.4 t c. Calculate the computed z or t value for the sample. x σ = 15/√36 = 2.5 minutes t = ( x μ29/ x = (46-40)/2.5 = 2.4 d. Explain whether or not the sample data provide evidence that the mean time needed to rotate and align a set of tires is greater than 40 minutes? Explain completely. Because the computed t = 2.4 is > t .10,35 = 1.69, we must reject the null hypothesis and conclude, with 90% confidence, that the mean time to rotate and align a set of tires is significantly greater than 40 minutes 3. The marketing director for an automobile manufacturer wants to determine the proportion of car customers that will purchase a special extended warranty for their new car. A random sample of 169 potential new car buyers was surveyed and, for the sample, only 20 expressed
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final exam solutions - ECON 2300 CUMULATIVE FINAL EXAM...

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