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University of Sharjah Industrial Engineering and Management Department 0405322: Engineering Statistics Term: Spring 2012-13 Date of Issue: Tuesday 05...

hi i need the answer of question 4

University of Sharjah Industrial Engineering and Management Department 0405322: Engineering Statistics Term: Spring 2012-13 Date of Issue: Tuesday 05 March ‘13 Date of Submission: Thursday 14 March ‘13 Homework-1 1. (05 points) A trucking firm suspects that the average lifetime of certain tires is at least 28,000 miles. To check the claim, the firm puts 40 of these tires on its trucks and gets a mean lifetime of 27,463 miles with a standard deviation of 1,348 miles. Should the firm conclude that the average lifetime of the tires is greater than 28,000 miles? Assume that the probability of type I error is to be at most 0.01? 2. (05 points) The specifications for a certain kind of ribbon call for a mean breaking strength of 180 pounds. If five pieces of the ribbon (randomly selected from the roll) have a mean breaking strength of 169.5 pounds with a standard deviation of 5.7 pounds, test whether the breaking strength is lower than 180 pounds at the 0.01 level of significance. 3. (05 Points) A sample of size 25 yielded mean equal to 33 and an estimated variance equal to 100. At the 1% level of significance would we have reasons to doubt the claim that the population mean is not greater than 27? What is the P- value? 4. (05 Points) In a study conducted in the forestry and wildlife department examined the influence of certain drug on the circulation levels of androgens in the blood. Blood samples from wild deer were obtained via the jaguar vein immediately after an intramuscular injection of the drug using darts and a capture gun. Deer were bled again approximately 30 minutes after the injection and then released. The levels of androgens at time of capture and 30 minutes later, measured in nanograms per milliliter (ng/ml), for 10 deer are as in the table. Assuming that the populations of androgen at time of injection and 30 minutes later are normally distributed, test at the 0.05 level of significance whether the androgen concentrations are altered after 30 minutes of restraint.
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Deer Androgen (ng/ml) At the time of injection Androgen (ng/ml) 30 minutes after injection 1 2.76 7.02 2 5.18 3.10 3 2.68 5.44 4 3.05 3.99 5 4.79 18.53 6 7.39 7.91 7 7.30 4.85 8 11.78 11.10 9 3.90 3.74 10 26.00 94.03 5. (05 Points) Two machines are used for filling plastic bottles with a net volume of 16.0 ounces. The filling volume can be assumed normal, with standard deviation σ 1 = 0.02 and σ 2 = 0.025 ounces. A member of the quality engineering staff suspects that both machines fill to the same mean net volume, whether or not this volume is 16.0 ounces. A random sample of 10 bottles is taken from the output of each machine (table). Do you think the engineer is correct? Use a level of significance of 0.05. Sample Machine-1 Machine-2 1 16.03 16.02 2 16.04 15.97 3 16.05 15.96 4 16.05 16.01 5 16.02 15.99 6 16.01 16.03 7 15.96 16.04 8 15.98 16.02 9 16.02 16.01 10 15.99 16.00
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