A bearing used in an automotive application is required to have a nominal inside diameter of 1.5 inches. A random sample of 25 bearings is selected and the average inside diameter of these bearings is 1.4975 inches. Bearing diameter is known to be normally distributed with standard deviation o = 0.01 inch. (a) Test the hypotheses Ho: μ = 1.5 versus H₁ : μ The true mean hole diameter (b) What is the P-value for the test in part (a)? P-value = i 1.5 using a = 0.01. significantly different from 1.5 in. at a = 0.01. (c) Compute the power of the test if the true mean diameter is 1.495 inches. Power of the test = i Round your answer to two decimal places (e.g. 98.76). bearings (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 be at least 0.90? Round your answer to two decimal places (e.g. 98.76). Statistical Tables and Charts

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 306.09 Newtons and 41.97 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.

DITO VOLTE 111 .ll ll OD: 26|| 8:10 TNT VOLTE B/s SLU SEA -.ODULE 6 Problem 3 A tire manufacturer claims that the average life of a certain grade of tire is greater than 25,000 miles under normal driving conditions on a car of a certain weight. A random sample of 15 tires is tested. A mean and standard deviation of 27,000 and 5000 miles, respectively, are computed. Assume that the lives of the tires in miles are approximately normally distributed. Can we conclude from these data that the manufacturer's product is as good as claimed? Use a .05 level of significance. Problem 4 A market research firm is interested in the amount that households in a certain town spend on RSIT

To compare the dry braking distances from 30 to 0 miles per hour for two makes of​ automobiles, a safety engineer conducts braking tests for 35 models of Make A and 35 models of Make B. The mean braking distance for Make A is 43 feet. Assume the population standard deviation is 4.7 feet. The mean braking distance for Make B is 44feet. Assume the population standard deviation is 4.5 feet. At α=0.10​, can the engineer support the claim that the mean braking distances are different for the two makes of​ automobiles? Assume the samples are random and​ independent, and the populations are normally distributed. Complete parts​ (a) through​ (e). a) identify the claim and state Ho and Ha b) find the critical values and identify the rejection regions c) Find the standardized test statistic z d) Decide whether to reject or fail to reject the null hypothesis. e) Interpret the decision in the context of the original claim.

A bearing used in an automotive application is required to have a nominal inside diameter of 1.5 inches. A random sample of 25 bearings is selected and the average inside diameter of these bearings is 1.4975 inches. Bearing diameter is known to be normally distributed 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 diameter significantly 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 be at least 0.91? bearings

A random sample of 76 eighth grade​ students' scores on a national mathematics assessment test has a mean score of 294. This test result prompts a state school administrator to declare that the mean score for the​ state's eighth graders on this exam is more than 285. Assume that the population standard deviation is 33. At α=0.13​, is there enough evidence to support the​ administrator's claim? Complete parts​ (a) through​ (e).       Question content area bottom Part 1 ​(a) Write the claim mathematically and identify H0 and Ha. Choose the correct answer below.     A. H0​: μ=285 Ha​: μ>285 ​(claim)   B. H0​: μ=285 ​(claim) Ha​: μ>285   C. H0​: μ≤285 Ha​: μ>285 ​(claim)   D. H0​: μ≥285 ​(claim) Ha​: μ<285   E. H0​: μ≤285 ​(claim) Ha​: μ>285   F. H0​: μ<285 Ha​: μ≥285 ​(claim) Part 2 ​(b) Find the standardized test statistic​ z, and its corresponding area.   z=enter your response here ​(Round to two decimal…

To compare the dry braking distances from 30 to 0 miles per hour for two makes of​ automobiles, a safety engineer conducts braking tests for 35 models of Make A and 35 models of Make B. The mean braking distance for Make A is 41 feet. Assume the population standard deviation is 4.6 feet.The mean braking distance for Make B is 42 feet. Assume the population standard deviation is 4.4 feet. At α=0.10​, can the engineer support the claim that the mean braking distances are different for the two makes of​ automobiles? Assume the samples are random and​ independent, and the populations are normally distributed. Complete parts​ (a) through​ (e).   (a) Identify the claim and state Ho and Ha. What is the​ claim? A.The mean braking distance is different for the two makes of automobiles. This is the correct answer. B.The mean braking distance is the same for the two makes of automobiles. C.The mean braking distance is less for Make A automobiles than Make B automobiles. Your answer is…

A national organization has been working with utilities throughout the nation to find sites for large wind machines that generate electricity. Wind speeds must average more than 13 miles per hour (mph) for a site to be acceptable. Recently, the organization conducted wind speed tests at a particular site. To determine whether the site meets the organization's requirements, consider the test, Ho: μ =13 Ha: μ >13 where  μ is the true mean wind speed at the site and a=.05  Suppose the observed significance level ( p-value) of the test is calculated to be p=0.4413   Interpret this result.     Since the p-value greatly exceeds α = .05, there is strong evidence to reject the null hypothesis.     Since the p-value exceeds α = .05, there is insufficient evidence to reject the null hypothesis.     We are 55.87% confident that μ = 13.     The probability of rejecting the null hypothesis is 0.4413.

A study of the longleaf pine trees in Wade Tract in Thomas County, Georgia measures the diameter at breast height (DBH) for each tree. This is the diameter of the tree at 4.5 feet and the units are in centimeters (cm). Only trees with DBH greater than 1.5 cm were sampled. A random sample of 40 trees had mean 27.9 cm and a standard deviation of 17.7 cm. We are interested in whether the mean DBH of the longleaf pine tree is greater than 25 cm. Test this claim. a. State the hypotheses for this problem. b. Calculate the value of the test statistic. c. Calculate and interpret the p-value. d. State your conclusion in terms of the problem.

To compare the dry braking distances from 30 to 0 miles per hour for two makes of​ automobiles, a safety engineer conducts braking tests for 35 models of Make A and 35 models of Make B. The mean braking distance for Make A is 43 feet. Assume the population standard deviation is 4.6 feet. The mean braking distance for Make B is 46 feet. Assume the population standard deviation is 4.5 feet. At α=0.10​, can the engineer support the claim that the mean braking distances are different for the two makes of​ automobiles? Assume the samples are random and​ independent, and the populations are normally distributed.   The critical​ value(s) is/are   Find the standardized test statistic z for μ1−μ2.