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 a mean, μ, of 1925 pounds, and a standard deviation of 100 pounds. It is claimed that an improvement in the manufacturing process has increased the mean breaking strength. To evaluate this claim, 70 newly manufactured cables are randomly chosen and tested, and their mean breaking strength is found to be 1936 pounds. Can we support, at the 0.05 level of significance, the claim that the mean breaking strength has increased? (Assume that the standard deviation has not changed.) Perform a one-tailed test. Then fill in the table below. Carry your intermediate computations to at least three decimal places, and round your responses as specified in the table. The null hypothesis: H0: The alternative hypothesis: H1: The type of test statistic: (Choose one) Z t Chi square F The value of the test statistic:(Round to at least three decimal places.) The…
The manager of a computer retails store is concerned that his suppliers have been giving him laptop computers with lower than average quality. His research shows that replacement times for the model laptop of concern are normally distributed with a mean of 3.3 years and a standard deviation of 0.6 years. He then randomly selects records on 31 laptops sold in the past and finds that the mean replacement time is 3.1 years.Assuming that the laptop replacement times have a mean of 3.3 years and a standard deviation of 0.6 years, find the probability that 31 randomly selected laptops will have a mean replacement time of 3.1 years or less.P(M < 3.1 years) = Enter your answer as a number accurate to 4 decimal places. NOTE: Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.Based on the result above, does it appear that the computer store has been given laptops of lower than average quality? No. The probability of obtaining this data is high enough…
The manager of a computer retails store is concerned that his suppliers have been giving him laptop computers with lower than average quality. His research shows that replacement times for the model laptop of concern are normally distributed with a mean of 3.2 years and a standard deviation of 0.5 years. He then randomly selects records on 35 laptops sold in the past and finds that the mean replacement time is 3 years.Assuming that the laptop replacment times have a mean of 3.2 years and a standard deviation of 0.5 years, find the probability that 35 randomly selected laptops will have a mean replacment time of 3 years or less.P(x-bar < 3 years) = Enter your answer as a number accurate to 4 decimal places. The amounts of nicotine in a certain brand of cigarette are normally distributed with a mean of 0.963 g and a standard deviation of 0.315 g. The company that produces these cigarettes claims that it has now reduced the amount of nicotine. The supporting evidence consists of a…
The manager of a computer retails store is concerned that his suppliers have been giving him laptop computers with lower than average quality. His research shows that replacement times for the model laptop of concern are normally distributed with a mean of 4.1 years and a standard deviation of 0.5 years. He then randomly selects records on 42 laptops sold in the past and finds that the mean replacement time is 3.9 years.Assuming that the laptop replacement times have a mean of 4.1 years and a standard deviation of 0.5 years, find the probability that 42 randomly selected laptops will have a mean replacement time of 3.9 years or less.P(M < 3.9 years)
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The manager of a computer retail store is concerned that his suppliers have been giving him laptop computers with lower than average quality. His research shows that replacement times for the model laptop of concern are normally distributed with a mean of 3.9 years and a standard deviation of 0.6 years. He then randomly selects records on 47 laptops sold in the past and finds that the mean replacement time is 3.7 years. Assuming that the laptop replacement times have a mean of 3.9 years and a standard deviation of 0.6 years, find the probability that 47 randomly selected laptops will have a mean replacement time of 3.7 years or less. P(M≤ 3.7 years) - Enter your answer rounded to 4 decimal places.
The manager of a computer retails store is concerned that his suppliers have been giving him laptop computers with lower than average quality. His research shows that replacement times for the model laptop of concern are normally distributed with a mean of 4.5 years and a standard deviation of 0.4 years. He then randomly selects records on 48 laptops sold in the past and finds that the mean replacement time is 4.4 years.Assuming that the laptop replacement times have a mean of 4.5 years and a standard deviation of 0.4 years, find the probability that 48 randomly selected laptops will have a mean replacement time of 4.4 years or less.P(M < 4.4 years) = Enter your answer as a number accurate to 4 decimal places. NOTE: Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.
A large financial company employs a human resources mamanger who is in charge of employe benefits. The manger wishes to estimate the average dental expenses per employee for the company. She selects a random sample of 60 employee records for the past year and determines that the sample mean of $492. Moreover, it is known from past studies that the population standard deviation for annual dental expenses is $74. Use this data to calculate a 95% cofidence interval for the mean expenses of all employees.
The breaking strengths of cables produced by a certain manufacturer have a mean, μ , of 1850 pounds, and a standard deviation of 50 pounds. It is claimed that an improvement in the manufacturing process has increased the mean breaking strength. To evaluate this claim, 100 newly manufactured cables are randomly chosen and tested, and their mean breaking strength is found to be 1864 pounds. Can we support, at the 0.1 level of significance, the claim that the mean breaking strength has increased? (Assume that the standard deviation has not changed.) Perform a one-tailed test. Then fill in the table below. Carry your intermediate computations to at least three decimal places, and round your responses as specified in the table. The null hypothesis: H0: The alternative hypothesis: H1: The type of test statistic: (Choose one)ZtChi squareF The value of the test statistic:(Round to at least three decimal places.)…

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