3) Estimating the Mean: Unknown Variancea) A student is working on his science fair project concerning the average height of a certainnative plant, which he believes is normally distributed. He finds 25 mature plants andmeasures their heights, and determines the average height to be 10.2 cm (s = 1.2 cm).Construct a 96% confidence interval on the mean height of the plants..<μ<. b) A sports team is interested in estimated the time required to complete a certain obstaclecourse. 30 athletes go through the course; the average completion time is 52 s (s = 4 s).Construct a 90% lower confidence bound on the average completion time of this obstaclecourse.μ>c) A company is interested in estimating the maximum weight that a certain machine canhandle safely. The weight capacity of this type of machine is normally distributed. Thecompany takes a random sample of 15 machines and finds that the sample mean weightcapacity is 1000 pounds (s = 50 pounds). Construct a 95% upper confidence bound on themaximum weight this machine can handle.μ<

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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The breaking strengths of cables produced by a certain manufacturer have historically had a mean of 1775 pounds and a standard deviation of 60 pounds. The company believes that, due to an improvement in the manufacturing process, the mean breaking strength, μ, of the cables is now greater than 1775 pounds. To see if this is the case, 90 newly manufactured cables are randomly chosen and tested, and their mean breaking strength is found to be 1788 pounds. Can we support, at the 0.05level of significance, the claim that the population mean breaking strength of the newly-manufactured cables is greater than 1775 pounds? Assume that the population standard deviation has not changed. Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places, and round your responses as specified below. a. State the null hypothesis H0 and the alternative hyposthesis H1. b. Find the value of the test statistic. c. Find the p-value. d. Can we…
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The breaking strengths of cables produced by a certain manufacturer have historically had a mean of 1800 pounds and a standard deviation of 90 pounds. The company believes that, due to an improvement in the manufacturing process, the mean breaking strength, μ, of the cables is now greater than 1800 pounds. To see if this is the case, 100 newly manufactured cables are randomly chosen and tested, and their mean breaking strength is found to be 1818 pounds. Can we support, at the 0.05 level of significance, the claim that the population mean breaking strength of the newly- manufactured cables is greater than 1800 pounds? Assume that the population standard deviation has not changed. Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places, and round your responses as specified below. (If necessary, consult a list of formulas.) (a) State the null hypothesis Ho and the alternative hypothesis H₁. H :O 1 (b) Determine the…
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The physical plant at the main campus of a large state university recieves daily requests to replace florecent lightbulbs. The distribution of the number of daily requests is bell-shaped and has a mean of 62 and a standard deviation of 4. Using the empirical rule (as presented in the book), what is the approximate percentage of lightbulb replacement requests numbering between 58 and 62?ans = %
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