A bearing used in an automotive application is required to have a nominal inside diameter of 1.5 inches. A random sample of 25bearings is selected and the average inside diameter of these bearings is 1.4975 inches. Bearing diameter is known to be normallydistributed with standard deviation o = 0.01 inch.(a) Test the hypotheses Ho:µ = 1.5 versus H1:µ + 1.5 using a = 0.01.The true mean hole diametersignificantly different from 1.5 in. at a = 0.01.(b) What is the P-value for the test in part (a)?P-value =Round your answer to two decimal places (e.g. 98.76).(c) Compute the power of the test if the true mean diameter is 1.495 inches.Power of the test =Round your answer to two decimal places (e.g. 98.76).(d) What sample size would be required to detect a true mean diameter as low as 1.495 inches if we wanted the power of the test to beat least 0.91?bearings

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Answered: A bearing used in an automotive…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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The daily sleep duration among college students is normally distributed with a mean of 8.13 and standard deviation of 1.87. You want to use a sample size such that 95% of the averages fall within ±15±15 minutes (.25 of an hour) of the true mean of 8.13. Determine the smallest number of students you need to sample.
An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 100 engines and the mean pressure was 4.9 lbs/square inch. Assume the standard deviation is known to be 0.7. If the valve was designed to produce a mean pressure of 4.7 lbs/square inch, is there sufficient evidence at the 0.02 level that the valve performs above the specifications? State the null and alternative hypotheses for the above scenario.
An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 200 engines and the mean pressure was 4.4 lbs/square inch. Assume the standard deviation is known to be 0.9. If the valve was designed to produce a mean pressure of 4.5 lbs/square inch, is there sufficient evidence at the 0.02 level that the valve performs below the specifications? State the null and alternative hypotheses for the above scenario.
on 5 of 21 The heights of women aged 20-29 in the United States are approximately Normal with mean 64.1 inches and standard deviation 3.7 inches. Men the same age have mean height 69.4 inches, with standard deviation 3.1 inches. Cheryl D. Fryar et al., "Anthropometric reference data for children and adults: United States, 2011-2014," Vital and Health Statistics, Series 3, no. 39 (August 2016), at www.cdc.gov/nchs. This report provides the means of various anthropometric measurements. Standard deviations were computed from the sample size and reported standard errors of the mean. Instructions on measuring upper arm length are in the National Health and Nutrition Examination Survey: Anthropometry Procedures Manual, January 2007. Side-by-Side O Macmillan Learning What is the z-score for a woman 5.5 feet tall? Give your answer to two decimal places. Z =
Suppose the mean IQ score of people in a certain country is 100. Suppose the director of a college obtains a simple random sample of 39 students from that country and finds the mean IQ is 104.5 with a standard deviation of 13.6. Complete parts (a) through (d) below. (a) Consider the hypotheses Ho: µ= 100 versus H,: µ> 100. Explain what the director is testing. Perform the test at the a = 0.10 level of significance. Write a conclusion for the test. Explain what the director is testing. Choose the correct answer below. O A. The director is testing if the sample provided sufficient evidence that the population mean IQ score is actually not equal to 100. OB. The director is testing if the sample provided sufficient evidence that the population mean IQ score is actually greater than 100. O C. The director is testing if the sample provided sufficient evidence that the population mean IQ score is actually not greater than 100. O D. The director is testing if the sample provided sufficient…
Tree-ring dates were used extensively in archaeological studies at Burnt Mesa Pueblo. At one site on the mesa, tree-ring dates (for many samples) gave a mean date of μ₁ = year 1259 with standard deviation ₁ = 35 years. At a second, removed site, the tree-ring dates gave a mean of μ₂ = year 1101 with standard deviation ₂ = 35 years. Assume that both sites had dates that were approximately normally distributed. In the first area, an object was found and dated as x₁ = year 1202. In the second area, another object was found and dated as x₂ = year 1246. The Standard Normal Distribution (u= 0, σ = 1) O -3 -2 O 0 68% of area 95% of area 99.7% of area 2 (a) Convert both X₁ and X₂ to z values, and locate both of these values under the standard normal curve of the figure above. (Round your answers to two decimal places.) Z1 = Z2 3 (b) Which of these two items is the more unusual as an archaeological find in its location? O x₁; the further a z value is from zero, the more unusual it is. X₂i the…
An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 200engines and the mean pressure was 5.4 pounds/square inch (psi). Assume the population standard deviation is 0.8 If the valve was designed to produce a mean pressure of 5.5psi, is there sufficient evidence at the 0.05 level that the valve does not perform to the specifications?
Suppose a certain dog breed has an average weight of 22.72 with a standard deviation of 4.30. What is the z-score of a dog whose length is 37.27? Answers should be correct to two decimal places.
A synthetic fiber used in manufacturing carpet has tensile strength that is normally distributed with mean 75.5 psi and standard deviation 3.5 psi. How is the standard deviation of the sample mean changed when the sample size is increased from n = 6 ton = 48 ? Round all intermediate calculations to four decimal places (e.g. 12.3456) and round the final answer to three decimal places (e.g. 98.768). The standard deviation is by i psi.
Acrylic bone cement is sometimes used in hip and knee replacements to fix an artificial joint in place. The force required to break an acrylic bone cement bond was measured for eight specimens under specified conditions, and the resulting mean and standard deviation were 306.11 newtons and 41.94 newtons, respectively. Assuming that it is reasonable to believe that breaking force under these conditions has a distribution that is approximately normal, estimate the mean breaking force for acrylic bone cement under the specified conditions using a 95% confidence interval. (Use a table or technology. Round your answers to three decimal places.) n USE SALT
A machine producesbearings with diameters that are normally distributed with mean 3.0005 inches and standard deviation of 0.0010 inch.Specifications require the bearing diameters to lie in the interval 3.000+-0.0020 inches.Those outside the intzerval are considered scrap and must be processed. With the existing machine setting, what fraction of total production will be scrap?

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