7 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 H:µ # 1.5 using a = 0.01.The true mean hole diameterv significantly different from 1.5 in. at a = 0.01.(b) What is the P-value for theisis not(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?bearingsStatistical Tables and Charts89°FCloudyeSC7.2.JLHKFIzx || CV.B. 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 Hj: 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 =iRound 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?ibearingsStatistical Tahles and Charts89°F10:47 A21-AprCloudy1713 )%2324967.3Y.KF

Answered: Image /qna-images/answer/a2827783-0adc-4519-ac18-6e544abaf0e8.jpg

Answered: A bearing used in an automotive…

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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Over a short period of time, a roller bearing manufacturer finds that 2% of the bearings exceed the USL diameter of 2.01 cm and 2% are less than the LSL of 1.99 cm. If the distribution ofdiameters is normal:a) What is the mean diameter?b) What is the standard deviation?c) What is Cp for the process?
The owner of a coin-operated hot coffee machine has received claims that there is an error in his machine, and it is not dispensing enough hot coffee into hand-held cups. He takes a random sample of 46 “8 oz servings” from a large number of servings and finds that the mean is 7.93 fluid ounces with a standard deviation of 0.38 ounces. Is this evidence of error in the machine if ? = 0.05? Use the P-Value method.
A study was conducted to see if increasing the substrate concentration has an appreciable effect on the velocity of a chemical reaction. With a substrate concentration of 1.6 moles per liter, the reaction was run 16 times, with an average velocity of 7.7 micromoles per 30 minutes and a standard deviation of 1.6. With a substrate concentration of 1.9 moles per liter, 12 runs were made, yielding an average velocity of 8.9 micromoles per 30 minutes and a sample standard deviation of 1.2. Is there any reason to believe that this increase in substrate concentration cause an increase in the mean velocity of the reaction of more than 0.5 micromole per 30 minutes? Use alpha 0.01
The average cost of tuition plus room and board for a small private liberal arts college is reported to be $8,500 per term, but a financial administrator believes that the average cost is higher. A study conducted using 350 small liberal arts colleges showed that the average cost per term is $8,745. The population standard deviation is $1,200. Let α = 0.05. What is the critical z-value for this test?
The average weight of a package of rolled oats is supposed to be at least 18 ounces. A sample of 18 packages shows a mean of 17.78 ounces with a standard deviation of 0.41. At alpha/a = .05, what is the decision rule?
A psychiatrist is testing a new antianxiety drug, which seems to have the potentially harmful side effect of lowering the heart rate. For a sample of 50 medical students whose pulse was measured after 6 weeks of taking the drug, the mean heart rate was 70 beats per minute (bpm). If the mean heart rate for a population was 72 bpm with a standard deviation of 12, can the psychiatrist conclude that the new drug lowers heart rate significantly? (Set the alpha level at .05)
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 six specimens under specified conditions, and the resulting mean and standard deviation were 306.03 newtons and 41.91 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
The men body mas index (BMI) for boys of age 12 years is 23.6kg/m An investigator wants to test if the BMI is higher in 12-year-old boys living in New York CIty. How many bos are needed to ensure that a two-sided test of hypothesis has 80% power to detect a difference in BMI of 2 kg/m? Assume that the standard deviation in BMI is 5.7 kg/m.
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 seven specimens under specified conditions, and the resulting mean and standard deviation were 306.15 newtons and 41.91 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. (Round your answers to three decimal places.)
According the U.S. Department of Education, full-time graduate students receive an average salary of $12,800. The dean of graduate studies at a large state university in PA claims that his graduate students earn more than this. He surveys 46 randomly selected students and finds their average salary is $13,445 with a standard deviation of $1800. With alpha = 0.05, is the dean’s claim correct?
The average expenditure per student (based on average daily attendance) for a certain school year was $10,337 with a population standard deviation of $1560. A survey for the next school year of 150 randomly selected students resulted in a sample mean of $10, 798. Find the P-value? Should the null hypothesis be rejected at alpha = .05 level of significance?
Before agreeing to purchase a large order of polyethylene sheaths for a particular type of high-pressure oil-filled submarine power cable, a company wants to see conclusive evidence that the true standard deviation of sheath thickness is less than 0.05 mm. What hypothesis should be tested, and why? In this context, what are the type I and type II errors?

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