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- Consider the following information on ultimate tensile strength (lb/in) for a sample of n = 4 hard zirconium copper wire specimens (from “Characterization Methods for Fine Copper Wire,” Wire J. Intl., Aug., 1997: 74-80): X (bar)= 76,831 s = 180 smallest xi = 76,683 largest xi = 77,048Determine the values of the two middle sample observations (and don’t do it by successive guessing!).A researcher estimates that the average height of the buildings of 30 or more stories in a large city is at most 700 feet. A random sample of 10 buildings is selected, and the heights in feet are shown. At α = 0.025, is there enough evidence to reject the claim? 485 511 841 725 615 520 535 635 616 582 What is the critical value of the t?The article in the ASCE Journal of Energy Engineering (1999, Vol. 125, pp.59-75) describes a study of the thermal inertia properties of autoclaved aerated concrete used as a building material. Five samples of the material were tested in a structure, and the average interior temperatures (°C) reported were as follows: 23.01, 22.22, 22.04, 22.62, and 22.59. Test that the average interior temperature is equal to 22.5°C using alpha (a) = 0.05. This problem is a test on what population parameter? What is the null and alternative hypothesis? What are the Significance level and type of test? What standardized test statistic will be used? What is the standard test statistic? What is the Statistical Decision? What is the statistical decision in the statement form?
- The tests of assumptions for yield gave values for Levene’s statistic and Shapiro-Wilk’s as 0.0562 and .00271, respectively. At a=0.05 , which statistical test is most appropriate to compare the yield among the nitrogen rates? a. Cochran’s Q B. Friedman’s C. Kruskal Wallis test . D. Anova F-testAn article in the Journal of Applied Polymer Science (Vol. 56, pp. 471–476, 1995) studied the effect of the mole ratio of sebacic acid on the intrinsic viscosity of copolyesters.- The data follows: Viscosity 0.45 0.2 0.34 0.58 0.7 0.57 0.55 0.44 Mole ratio 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 (a) Construct a scatter diagram of the data.The article “Withdrawal Strength of Threaded Nails” (D. Rammer, S. Winistorfer, and D. Bender, Journal of Structural Engineering 2001:442–449) describes an experiment comparing the ultimate withdrawal strengths (in N/mm) for several types of nails. For an annularly threaded nail with shank diameter 3.76 mm driven into spruce-pine-fir lumber, the ultimate withdrawal strength was modeled as lognormal with μ = 3.82 and σ = 0.219. For a helically threaded nail under the same conditions, the strength was modeled as lognormal with μ = 3.47 and σ = 0.272. a) What is the mean withdrawal strength for annularly threaded nails? b) What is the mean withdrawal strength for helically threaded nails? c) For which type of nail is it more probable that the withdrawal strength will be greater than 50 N/mm? d) What is the probability that a helically threaded nail will have a greater withdrawal strength than the median for annularly threaded nails? e) An experiment is performed in which withdrawal…
- An article includes the accompanying data on compression strength (lb) for a sample of 12-oz aluminum cans filled with strawberry drink and another sample filled with cola. Beverage Sample Size Sample Mean Sample SD Strawberry Drink 10 535 24 Cola 10 559 15 Does the data suggest that the extra carbonation of cola results in a higher average compression strength? Base your answer on a P-value. (Use ? = 0.05.) State the relevant hypotheses. (Use ?1 for the strawberry drink and ?2 for the cola.) H0: ?1 − ?2 = 0Ha: ?1 − ?2 ≥ 0H0: ?1 − ?2 = 0Ha: ?1 − ?2 ≠ 0 H0: ?1 − ?2 = 0Ha: ?1 − ?2 < 0H0: ?1 − ?2 = 0Ha: ?1 − ?2 > 0 Calculate the test statistic and determine the P-value. (Round your test statistic to one decimal place and your P-value to three decimal places.) t = P-value = State the conclusion in the problem context. Reject H0. The data suggests that cola has a higher average compression strength than the strawberry drink.Reject H0. The…Use the following data to determine if drug B produces higher creatinine levels than drug A, assume the data is normally distributed. Creatinine levels (µmol/L) Drug A Drug B 48.2 52.3 54.6 57.4 58.3 55.6 47.8 53.2 51.4 61.3 52.0 58.0 55.2 59.8 49.1 54.8 49.9 52.6 Write out the null and alternative hypothesis in *words and symbols*. What is the hypothesis in words? Determine the critical value (use a significance level of 0.05) Calculate the test statistic, and determine if the results are significant or not. How did you calculate the standard deviations? Please provide a complete outline of calculationsResearchers interested in lead exposure due to car exhaust sampled the blood of 52 police officers subjected to constant inhalation of automobile exhaust fumes while working traffic enforcement in a primarily urban environment. The blood samples of these officers had an average lead concentration of 124.32 µg/l and a SD of 37.74 µg/l; a previous study of individuals from a nearby suburb, with no history of exposure, found an average blood level concentration of 35 µg/l. Test the hypothesis that the downtown police officers have a higher lead exposure than the group in the previous study. Interpret your results in context. Based on your preceding result, without performing a calculation, would a 99% confidence interval for the average blood concentration level of police officers contain 35 µg/l? Based on your preceding result, without performing a calculation, would a 99% confidence interval for this difference contain 0? Explain why or why not.
- If X1 and X2 constitute a random sample of size n = 2from an exponential population, find the efficiency of 2Y1relative to X, where Y1 is the first order statistic and 2Y1and X are both unbiased estimators of the parameter1)A new starch polymer foam with high shock absorbent properties is expected to perform better thanthe old foam which can withstand a maximum impact of 1.56 Joule (J). A simple destructive testto quantify shock absorption ability of the new foam is conducted. Table 5 shows the impact energyabsorbed (in J) that the new foam can withstand for each test. Table 51.61 1.5 1.65 1.7 1.4 1.59 1.65 1.5 Does the recorded data suggests that the new foam performs better than the old foam? Use 2.5%level of significance. 2) A number of 28 university students who smokes completed a questionnaire inquiring their smokinghistory and behavior. The result shows that the average smoking initiation age of this group is 21.6years with a variance of 18.49. Based on past record, the smoking initiation age of universitystudent has a mean of 20.74 years with a standard deviation of 5.1 years. Conduct a necessaryanalysis to determine if the smoking initiation age remain the same as the previous record.…Researchers interested in lead exposure due to car exhaust sampled the blood of 52 police officers subjected to constant inhalation of automobile exhaust fumes while working traffic enforcement in a primarily urban environment. The blood samples of these officers had an average lead concentration of 124.32 µg/l and a SD of 37.74 µg/l; a previous study of individuals from a nearby suburb, with no history of exposure, found an average blood level concentration of 35 µg/l. Based on your preceding result, without performing a calculation, would a 99% confidence interval for the average blood concentration level of police officers contain 35 µg/l? Based on your preceding result, without performing a calculation, would a 99% confidence interval for this difference contain 0? Explain why or why not.
