During the manufacture of the driver gear of an automobile, a dial bore gauge is used to bore a hole into cast steel. Specifications require that the diameter of the bore hole be between 204.05 and 205.05 millimeters, with a target mean of 205 millimeters. The International Journal of Quality Research (Vol. 8, 2014) applied capability analysis to assess the performance of the boring operation. Five driver gear parts were sampled each hour for 20 consecutive hours, and the bore diameter of each part was determined. The data are presented in the file BORE.xlsx. Run a complete capability analysis on the data. How would you categorize the performance of the boring process? Is the process under control. Find the capability index and plot the X-bar chart to support your argument.
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- The article “Wind-Uplift Capacity of Residential Wood Roof-Sheathing Panels Retrofitted with Insulating Foam Adhesive” (P. Datin, D. Prevatt, and W. Pang, Journal of Architectural Engineering, 2011:144–154) presents a study of the failure pressures of roof panels. A sample of 15 panels constructed with 8-inch nail spacing on the intermediate framing members had a mean failure pressure of 8.38 kPa with a standard deviation of 0.96 kPa. A sample of 15 panels constructed with 6-inch nail spacing on the intermediate framing members had a mean failure pressure of 9.83 kPa with a standard deviation of 1.02 kPa. Can you conclude that 6-inch spacing provides a higher mean failure pressure?A quality control expert at a local dairy claims that its cartoons contain more than 64oz of milk a sample of 15 cartoons reveals a mean of 65 and 1.1 oxs respectively. At the 1% level, does the appropriate hypothesis support his claim? find and interpret the p valueThe article “Approximate Methods for Estimating Hysteretic Energy Demand on PlanAsymmetric Buildings” (M. Rathhore, A. Chowdhury, and S. Ghosh, Journal of Earthquake Engineering, 2011: 99–123) presents a method, based on a modal pushover analysis, of estimating the hysteretic energy demand placed on a structure by an earthquake. A sample of 18 measurements had a mean error of 457.8 kNm with a standard deviation of 317.7 kNm. An engineer claims that the method is unbiased, in other words, that the mean error is 0. Can you conclude that this claim is false?
- Groups of non-smokers who were not exposed to smoke and non-smokers who were exposed to secondhand smoke were sampled to test their cotinine levels (ng/mL). Using a 0.05 significance level, test the claim that non-smokers exposed to tobacco smoke have higher mean cotinine levels than non-smokers that are not exposed. Exposed to secondhand smoke: n=40, x̅=60.58, s=138.08 Not exposed to secondhand smoke: n=40, x̅=16.35, s=62.53 1. H^0=? 2. H^1=? 3. Critical value(s):? 4. Graph rejection regions with labelled critical value(s) 5. Test statistic: State what test stat is being used (z,t,etc.) the formula being used, and what values are substituted into the formula. 6. P-value=? 7. State the conclusion of the test in the context of the problem (for example, not just "reject null" but what does it mean for this specific problem):. A new drug for pain relief is being tested within a given palliative care population. The new drug is being compared to an already approved pain relief drug that is commonly used in providing palliative care to patients who experience chronic severe pain. Assume the patients are asked to rate the pain on a scale from 1 to 10, and the data presented below was obtained from a small study designed to compare the effectiveness of the two drugs. Set up and interpret the results of a Mann-Whitney Utest with an alpha of .05. Pain Rating as Reported by Patients Old Drug13346 New Drug12337 Old Drug New Drug Total Sample (Ordered Smallest to Largest) Ranks Old Drug New Drug Old Drug New Drug…An automobile manufacturer who wishes to advertise that one of its models achieves 30 mpg (miles per gallon) decides to carry out a fuel efficiency test. Six nonprofessional drivers were selected, and each one drove a car from Phoenix to Los Angeles. The resulting fuel efficiencies (in miles per gallon) are given below. 27.2 29.2 31.2 28.5 30.3 29.5 Assuming that fuel efficiency is normally distributed under these circumstances, do the data contradict the claim that true average fuel efficiency is (at least) 30 mpg? Test the appropriate hypotheses at significance level 0.05. (Use a statistical computer package to calculate the P-value. Round your test statistic to two decimal places and your P-value to three decimal places.) t= P-value = State the conclusion in the problem context. Reject H0. We have convincing evidence that the mean fuel efficiency under these circumstances is less than 30 miles per gallon.Do not reject H0. We have convincing evidence that the mean fuel…
- The article “Wind-Uplift Capacity of Residential Wood Roof-Sheathing Panels Retrofitted with Insulating Foam Adhesive” (P. Datin, D. Prevatt, and W. Pang, Journal of Architectural Engineering, 2011:144–154) presents a study of the failure pressures of roof panels. Following are the failure pressures, in kPa, for five panels constructed with 6d smooth shank nails. These data are consistent with means and standard deviations presented in the article. 3.32 2.53 3.45 2.38 3.01 Find a 95% confidence interval for the mean failure pressure for this type of roof panel.A simple random sample of front-seat occupants involved in car crashes is obtained. Among3000occupants not wearing seat belts,36were killed. Among 7697occupants wearing seat belts,18were killed. Use a0.05significance level to test the claim that seat belts are effective in reducing fatalities. Complete parts (a) through (c) below.From a random sample of 1000 Americans, it was discovered that 920 of them lived in neighborhoods with acceptable levels of Carbon Monoxide. (Source: The Environmental Protection Agency) Obtain a point estimate for the proportion of Americas who live in neighborhoods with acceptable levels of carbon monoxide.
- Tardigrades, or water bears, are a type of micro-animal famous for their resilience. In examining the effects of radiation on organisms, an expert claimed that the amount of gamma radiation needed to sterilize a colony of tardigrades no longer has a mean of 900 Gy (grays). (For comparison, humans cannot withstand more than 10 Gy .) A study was conducted on a sample of 27 randomly selected tardigrade colonies, finding that the amount of gamma radiation needed to sterilize a colony had a sample mean of 907 Gy , with a sample standard deviation of 17 Gy . Assume that the population of amounts of gamma radiation needed to sterilize a colony of tardigrades is approximately normally distributed. Complete the parts below to perform a hypothesis test to see if there is enough evidence, at the 0.05 level of significance, to support the claim that μ , the mean amount of gamma radiation needed to sterilize a colony of tardigrades, is not equal to 900…Tardigrades, or water bears, are a type of micro-animal famous for their resilience. In examining the effects of radiation on organisms, an expert claimed that the amount of gamma radiation needed to sterilize a colony of tardigrades no longer has a mean of 900 Gy (grays). (For comparison, humans cannot withstand more than 10 Gy .) A study was conducted on a sample of 27 randomly selected tardigrade colonies, finding that the amount of gamma radiation needed to sterilize a colony had a sample mean of 907 Gy , with a sample standard deviation of 17 Gy . Assume that the population of amounts of gamma radiation needed to sterilize a colony of tardigrades is approximately normally distributed. Complete the parts below to perform a hypothesis test to see if there is enough evidence, at the 0.05 level of significance, to support the claim that μ , the mean amount of gamma radiation needed to sterilize a colony of tardigrades, is not equal to 900…The Excel file Room Inspection provides data for 100 room inspections at 25 hotels in a major chain. Management would like the proportion of nonconforming rooms to be less than 2%. Test an appropriate hypothesis to determine if management can make this claim.