The specification for the diameters of ball bearings is 15.40–15.60 mm. Data from an X chart, based on samples of size 8, that shows that the process is in control, yield values of X = 15.52 and R = 0.05- Compute the value of Cpk for this process. b. Is the process capability acceptable? Explain. a.
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- 10. A pharmacist attempts to weigh 120 mg of codeine sulfate on a balance with a sensitivity requirement of 6 mg. Calculate the maximum potential error in terms of percentage.In experiments to determine the effectiveness of drugs such as anti-fungal ointments that are applied to the skin, the concentration of the drug in a patient’s skin must be measured. The article “Determining Bioequivalence of Topical Dermatological Drug Products by Tape- Stripping” (W. Navidi, A. Hutchinson, et al., Journal of Pharmacokinetics and Pharmacodynamics, 2008:213–220) describes an improved method of measuring that is designed to ensure that all the drug in the skin is recovered. Assume that in an experiment using the old method, the mean amount of drug recovered from a sample of 49 patients was 105 ng with a standard deviation of 20 ng, and that in an experiment using the new method the mean amount of drug recovered in a sample of 35 patients was 117 ng with a standard deviation of 15 ng. Find a 98% confidence interval for the difference in the mean amounts recovered between the two methods.A law enforcement organization claims that their radargun is accurate to within 0.5 miles per hour for a courthearing. An independent organization hired to test theaccuracy of the radar gun conducted 12 tests on a projectilemoving at 60 miles per hour. Given the data inthe following table, determine if the radar gun can beused in court. State the hypothesis and base your commentson an appropriate α level.
- Life-saving drug: Penicillin is produced by the Penicillin fungus, which is grown in a broth whose sugar content must be carefully controlled. Several samples of broth were taken on three successive days, and the amount of dissolved sugars, in milligrams per milliliter, was measured on each sample. The results were as follows.Calculate the average values of the Cp and Cpk capabil-ity indices for the BOD data , assuming that LSL=5 mg/L and USL=35 mg/L. Do these val-ues of the indices indicate that the process performance is satisfactory?The sulfate ion concentration in natural water can be determined by measuring the turbidity that results when an excess of BaCl2 is added to a measured quantity of the sample. A turbiditimeter, the instrument used for this analysis, was calibrated with a series of standard Na2SO4 solutions. The following data were obtained for the calibration:
- In the 2015 AFC Championship game, there was a charge that the New England Patriots underinflated their footballs for an advantage. The Patriots' opponents during the championship game were the Indianapolis Colts. Measurements of the Colts' footballs were taken. The balls should be inflated to between 12.5 and 13.5 pounds per square inch (psi). The accompanying data consists of six of the eight measurements on the Colts' footballs. Complete parts (a) and (b) below. 12.75, 12.50, 12.15, 12.35, 12.55, 12.30 The test statistic is = (Round to two decimal places as needed.) The p-value is = (Round to three decimal places as needed.) b. Use the data to construct a 95% confidence interval for the mean psi for the Colts' footballs. How does this confidence interval support your conclusion in part (a)? The 95% confidence interval is ___ psi to ___ psi. (Round to two decimal places as needed. Use ascending order.)A pharmaceutical company states that there is 500mg of active ingredient in each capsule for one of the medicines they manufacture. However, the FDA believes the company is purposely underfilling the capsule to save money. A sample of 20 capsules is taken and the amount of active ingredient inside is measured. The results are below: 484 460 471 512 494 529 494 485 474 502 503 538 466 495 475 529 518 464 449 489 Part 1: Construct a 95% confidence interval using toolPAK for the amount of active ingredient measured. Use the appropriate distribution, and specify the upper and lower limits of the interval. Part 2: Carefully interpret the 95% confidence interval? What if you did constructed a Confidence Interval Manually? Part 3: Does the 95% confidence interval support the FDA’s claim? Explain. Part 4: Would your answer change if the confidence level was lowered to 75%? Explain.A series of tests of fire prevention sprinkler systems that use a foaming agent to quell the fire were performed to determine how long it took (in seconds) for the sprinklers to be activated after the detection of a fire by the system. The system has been designed so that the true average activation time is supposed to be at most 25 seconds. Do the data strongly indicate that the design specifications have not been met? The data for the test are given below: 27 41 22 27 23 35 30 33 24 27 28 22 24
- In a study of exhaust emissions from school buses, the pollution intake by passengers was determined for a sample of nine school buses used in the Southern California Air Basin. The pollution intake is the amount of exhaust emissions, in grams per person, that would be inhaled while traveling on the bus during its usual 1818‑mile trip on congested freeways from South Central LA to a magnet school in West LA. (As a reference, the average intake of motor emissions of carbon monoxide in the LA area is estimated to be about 0.0000460.000046 grams per person.) The amounts for the nine buses when driven with the windows open are given. 1.151.15 0.330.33 0.400.40 0.330.33 1.351.35 0.380.38 0.250.25 0.400.40 0.350.35 A good way to judge the effect of outliers is to do your analysis twice, once with the outliers and a second time without them. Give two 90%90% confidence intervals, one with all the data and one with the outliers removed, for the mean pollution intake among all school buses…The sides of a rectangle measure 5 ± 1 (cm) and 8 ± 2 (cm). How much is your area worth?Consider the statistical hypothesis to calculate the propagation of errorsAn ecologist hypothesizes that birds with longer wing spans use wider tree branches. The ecologist captured male birds, measured their wing span and other characteristics in millimeters, and then marked and released them. During the ensuing winter, the ecologist repeatedly observed the marked birds as they foraged for food on tree branches. He noted the branch diameter on each occasion, and calculated the average branch diameter for each bird in centimeters. The measurement data are below. What can the ecologist conclude with an α of 0.05 wing span branch diameter 79.380.180.781.579.580.781.180.580.7 1.561.531.391.041.391.021.211.311.21 A) What is the appropriate statistic? Then Compute the statistic B) Compute the appropriate test statistic(s) for H1: ρ > 0 critical value = test statistic= C) Effect Size