Consider the following sample of observations on coating thickness for low-viscositypaint (“Achieving a Target Value for a Manufacturing Process: A Case Study," J.Qual. Technol., 1992: 22-26):0.83 0.88 0.88 1.04 1.09 1.12 1.29 1.311.48 1.49 1.59 1.62 1.65 1.71 1.76 1.83Assume that the distribution of coating thickness is normal (a normal probability plotstrongly supports this assumption)(a) Calculate a point estimate of the mean value of coating thickness, and state whichestimator you used.(b) Calculate a point estimate of the median of the coating thickness distribution,and state which estimator you used.(c) Calculate a point estimate of the value that separates the largest 10% of all valuesin the thickness distribution from the remaining 90%, and state which estimatoryou used. [Hint: Express what you are trying to estimate in terms of u and o](d) Estimate Pr(X < 1.5), i.e., the proportion all thickness values less than 1.5. [Hint:If you knew the values of u and o, you could calculate this probability. Thesevalues are not available, but they can be estimated.]

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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 authors of the article “Predictive Model for PittingCorrosion in Buried Oil and Gas Pipelines”(Corrosion, 2009: 332–342) provided the data on whichtheir investigation was based.a. Consider the following sample of 61 observations onmaximum pitting depth (mm) of pipeline specimensburied in clay loam soil. 0.41 0.41 0.41 0.41 0.43 0.43 0.43 0.48 0.480.58 0.79 0.79 0.81 0.81 0.81 0.91 0.94 0.941.02 1.04 1.04 1.17 1.17 1.17 1.17 1.17 1.171.17 1.19 1.19 1.27 1.40 1.40 1.59 1.59 1.601.68 1.91 1.96 1.96 1.96 2.10 2.21 2.31 2.462.49 2.57 2.74 3.10 3.18 3.30 3.58 3.58 4.154.75 5.33 7.65 7.70 8.13 10.41 13.44Construct a stem-and-leaf display in which the twolargest values are shown in a last row labeled HI.b. Refer back to (a), and create a histogram based oneight classes with 0 as the lower limit of the firstclass and class widths of .5, .5, .5, .5, 1, 2, 5, and 5,respectively.c. The accompanying comparative boxplot fromMinitab shows plots of pitting depth for four differenttypes of soils.…
Consider the following sample observations on stabilized viscosity of asphalt specimens. 2,762 2,907 3,012 2,813 2,876 Suppose that for a particular application, it is required that true average viscosity be 3,000. Does this requirement appear to have been satisfied? State the appropriate hypotheses. (Use ? = 0.05.) H0: ? > 3,000 Ha: ? < 3,000 H0: ? = 3,000 Ha: ? ≠ 3,000 H0: ? ≠ 3,000 Ha: ? = 3,000 H0: ? < 3,000 Ha: ? = 3,000 Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to three decimal places.) t = P-value = What can you conclude? Reject the null hypothesis. There is sufficient evidence to conclude that the true average is viscosity differs from 3000.Do not reject the null hypothesis. There is sufficient evidence to conclude that the true average is viscosity differs from 3000. Reject the null hypothesis. There is not sufficient evidence to conclude that…
The article “Hydrogeochemical Characteristics of Groundwater in a Mid-Western CoastalAquifer System” (S. Jeen, J. Kim, et al., Geosciences Journal, 2001:339–348) presentsmeasurements of various properties of shallow groundwater in a certain aquifer system inKorea. Following are measurements of electrical conductivity (in microsiemens percentimeter) for 23 water samples.2099 528 2030 1350 1018 384 14991265 375 424 789 810 522 513488 200 215 486 257 557 260461 500Find the mean.Find the standard deviation.Find the median.Construct a dotplot.Find the 10% trimmed mean.Find the first quartile.Find the third quartile.Find the interquartile range.Construct a boxplot.Which of the points, if any, are outliers?If a histogram were constructed, would it be skewed to the left, skewed to the right, orapproximately symmetric?
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?
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.
CONSIDER that the data is UNCORRELATED use alpha .05. Provide the following: 1. CI of the F value 2. Statistical Interpretation
Following are the protein contents measured in two types of species:Species 1: 0.72 1.12 0.81 0.89 0.72 0.81 1.01 0.75 0.83Species 2: 1.21 0.93 0.80 1.12 1.22 0.94 0.87 i) Assuming normality, test the hypothesis that the two species have the sameaverage protein contents by using 5-step hypothesis testing procedure at 5 %level of significance, and using the critical values approach.ii) Calculate the p-value of this test and make decision.iii) Write down the standard error of this test and calculate its numerical value ?
Lactation promotes a temporary loss of bone mass to provide adequate amounts of calcium for milk production. The paper “Bone Mass Is Recovered from Lactation to Postweaning in Adolescent Mothers with Low Calcium Intakes” (Amer. J. of Clinical Nutr., 2004: 1322–1326) gave the following data on total body bone mineral content (TBBMC) (g) for a sample both during lactation (L) and in the postweaning period (P). SubjectL 1928 2549 2825 1924 1628 2175 2114 2621 1843 2541P 2126 2885 2895 1942 1750 2184 2164 2626 2006 2627 Does the data suggest that true average total body bone mineral content during postweaning exceeds that during lactation by more than 25 g? State and test the appropriate hypotheses using a significance level of .05.
An article reports the following values for soil heat flux of eight plots covered with coal dust. 37.9 37.8 37.9 35.1 35.5 27.5 18.3 24.1 The mean soil heat flux for plots covered only with grass is 29.0. Assuming that the heat-flux distribution is approximately normal, does the data suggest that the coal dust is effective in increasing the mean heat flux over that for grass? Test the appropriate hypotheses using ? = 0.05.State the appropriate hypotheses. H0: ? = 29Ha: ? > 29H0: ? = 29Ha: ? < 29 H0: ? = 29Ha: ? ≠ 29H0: ? ≠ 29Ha: ? = 29 Calculate the test statistic and determine 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 the null hypothesis. There is sufficient evidence to conclude that there was an increase in mean heat flux.Do not reject the null hypothesis. There is sufficient evidence to conclude that…
Listed below are amounts of strontium-90 (in millibecquerels, or mBq, per gram of calcium) in a simple random sample by baby teeth obtained from Pennsylvania residents and New York residents born after 1979. Use a 0.05 significance level and Wilcoxon rank-sum test to test the claim that the median amount of strontium-90 from Pennsylvania residents is the same as the median from New York residents. Pennsylvania 155 142 149 130 151 163 151 142 156 133 138 161 New York 133 140 142 131 134 129 128 140 140 140 137 143 1. what is the exact value of R = R 1 (Pennsylvania)? (Round off to 1 decimal place.) 2. what is the value of μ R ? (Type as a whole number.) 3. what is the value of σ R ? (Round off to 2 decimal places.) 4. what is the computed value of z ? (Round off to 2 decimal places.) 5. what is the tabular value of z ? (Round off to 2 decimal places.
An article reports the following values for soil heat flux of eight plots covered with coal dust. 37.3 36.8 37.3 32.1 33.4 26.5 18.1 24.8 The mean soil heat flux for plots covered only with grass is 29.0. Assuming that the heat-flux distribution is approximately normal, does the data suggest that the coal dust is effective in increasing the mean heat flux over that for grass? Test the appropriate hypotheses using α = 0.05. Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to three decimal places.) t = P-value
The article “Measuring and Understanding the Aging of Kraft Insulating Paper in Power Transformers” (IEEE Electrical Insul. Mag., 1996: 28– 34) contained the following observations on degree of polymerization for paper specimens for which viscosity times concentration fell in a certain middle range: 418, 434, 454, 421, 437, 463, 421, 439, 465, 422, 446, 425, 447, 427, 448, 431, 453 (a) Calculate a 99% confidence interval for the true average degree of polymerization. (b) Does the confidence interval suggest that μ = 435 is a plausible value for the true average degree of polymerization? (c) Does the confidence interval suggest that μ = 460 is a plausible value for the true average degree of polymerization?

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