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In an experiment to compare the tensile strengths of I = 5 different types of copper wire, J = 4 samples of each type were used. The between-samples and within-samples estimates of
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Chapter 10 Solutions
Probability and Statistics for Engineering and the Sciences
- A random sample of 50 students was asked to estimate how much money they spent on textbooks in a year. The sample skewness of these amounts was found to be 0.83 and the sample kurtosis was 3.98. Test at the 10% level the null hypothesis that the population dis- tribution of amounts spent is normal.arrow_forwardAssuming all other factors are held constant, if the df value for a two-tailed t-test with a = .05 were increased from df =6 to df = 20, what would happen to the critical values for t?arrow_forwardConsider 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!).arrow_forward
- A researcher hypothesizes that in a certain country the net annual growth of private sector purchases of government bonds, B, is positively related to the nominal rate of interest on the bonds, NI, and negatively related to the rate of inflation Π: Bt = a0 + a1NIt + a2Π t + ut Note that it may be hypothesized that B depends on the real rate of interest on bonds, R, where R = NI – Π. Using a sample of 56 annual observations, s/he estimates the following equations: (1) Bt = 0.43 + 0.90NIt - 0.97Πt R21 = 0.962, SSR1 = 2.20, QRESET(F1,52) = 16.6 (3.58) (8.80) (-1.05) (2) Bt = 0.44 + 0.94Rt R22 = 0.960, SSR2 = 2.22, QRESET(F1,53) = 0.9 (9.70) (16.7) (3) Bt = 0.44 + 1.14NIt SSR3 = 9.20, QRESET(F1,53) = 59.9 (8.84) (36.1) (4) NIt = 0.08 + 0.94Πt R24 = 0.997, SSR4 = 0.18, QRESET(F1,53) = 1.4…arrow_forwardAn 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…arrow_forwardResearchers 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.arrow_forward
- 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…arrow_forwardUse 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 calculationsarrow_forwardConsider the following summary data on the modulus of elasticity (✕ 106 psi) for lumber of three different grades. Grade J xi. si 1 9 1.61 0.21 2 9 1.55 0.25 3 9 1.44 0.23 Use this data and a significance level of 0.01 to test the null hypothesis of no difference in mean modulus of elasticity for the three grades. Calculate the test statistic. (Round your answer to two decimal places.) f = What can be said about the P-value for the test? P-value > 0.100 0.050 < P-value < 0.100 0.010 < P-value < 0.050 0.001 < P-value < 0.010 P-value < 0.001 What can you conclude? Reject H0. At least two of the three grades appear to differ significantly. Reject H0. The three grades do not appear to differ significantly. Fail to reject H0. The three grades do not appear to differ significantly. Fail to reject H0. At least two of the three grades appear to differ significantly.arrow_forward
- L12Q5.At 10% level of significance, the critical value(s) of z to test H0: μ1= μ2; against Ha: μ1 ≠ μ2 is/arearrow_forwardGiven the Data:Test the hypothesis that p(rho)xy is not equal to 0 at the 0.05 level of significance.arrow_forwardA 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 24arrow_forward
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