Samples of plastic product were selected from a batch of material, and the tensile strength in kg was measured for three different time durations, with the following results. UTM UTM i. Time durations Tensile strength 11-12 pm THUY 12-1 pm UT 605 602 375 704 465 287 1-2 pm 680 601 602 478 438 370 512 535 590 501 394 473 Estimate the variability due to time durations of tensile strength and the overall variability UTM of the observations. ii. Is there a significance difference in the tensile strength due to different time durations? Use 1% significance level. UTM UTM
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- 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. 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.A study of Spring Peeper breeding yielded the results in the table below. Spring Peepers were bred in different temperature controlled environments. The concentration of dissolved oxygen was measured in each environment. Temperature of water (⁰C) Dissolved oxygen in freshwater (mg/L) Number of eggs hatched into tadpoles 8 10.0 80 8 12.0 100 8 13.5 120 8 16.0 150 15 8.0 600 15 9.5 1090 15 12.0 1700 15 14.0 2190 22 6.5 870 22 8.5 1450 22 10.5 1970 22 12.0 2450 29 5.5 110 29 7.0 210 29 9.0 400 29 11.0 500 Graph the data in the table linked in the description above. (Hint: You must identify the dependent variable and two independent variables.) You may complete your graph electronically or by hand (then take a photo of your graph). Upload your photo or electronic file. (COMPLETE IN ONE GRAPH).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…
- Breast feeding sometimes results in a temporary loss of bone mass as calcium is depleted in the mother's body to provide for milk production. An investigation gave the following data on total body bone mineral content (g) for a sample of mothers both during breast feeding (B) and in the postweaning period (P). Subject 1 2 3 4 5 6 7 8 9 10 B 2170 1840 2563 2348 2721 2601 2386 2640 2549 1852 P 2300 1994 2594 2523 2852 2774 2534 2829 2578 2039 Do the data suggest that true average total body bone mineral content during postweaning exceeds that during breast feeding by more than 25 g? State and test the appropriate hypotheses using a significance level of 0.05. (Use a statistical computer package to calculate the P-value. Use ?P − ?B. Round your test statistic to two decimal places and your P-value to three decimal places.) t = df = P-value = Conclusion Fail to reject H0. OR Reject H0.The Turbine Oil Oxidation Test (TOST) and the Rotating Bomb Oxidation Test (RBOT) are two different procedures for evaluating the oxidation stability of steam turbine oils. An article reported the accompanying observations on x = TOST time (hr) and y = RBOT time (min) for 12 oil specimens. TOST 4200 3600 3750 3650 4050 2770 RBOT 370 345 375 315 350 205 TOST 4870 4525 3450 2700 3750 3325 RBOT 400 380 285 220 345 290 (a) Calculate the value of the sample correlation coefficient. (Round your answer to four decimal places.) r = Carry out a test of hypotheses to decide whether RBOT Time and TOST time are linearly related. (Use ? = 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 =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.
- Kaitlyn measures the upload speed in megabits per second of her home broadband internet connection during peak hours and off-peak hours. The results are provided in the accompanying table. Peak Off-Peak 5.83 5.14 6.05 6.80 7.14 6.98 3.54 5.77 5.45 7.27 5.90 6.62 5.81 6.19 4.82 6.08 6.37 6.59 4.65 5.58 5.30 7.41 6.48 6.26 5.96 6.37 5.79 6.31 6.84 6.55 5.06 4.95 5.61 7.03 6.45 6.77 Examine the results of Kaitlyn's test to determine the statements that compare the medians and interquartile ranges of the data sets to each other in terms of this situation. Select the two correct answers. The median upload speed during peak hours is 5.905 megabits per second, which is less than the median upload speed during off-peak hours, 7.005 megabits per second. The upload speeds during peak hours are slower on average compared to off-peak times. The median upload speed during peak hours is 6.37 megabits per second, which is greater than the median upload speed during…The efficiency ratio for a steel specimen immersed in a phosphating tank is the weight of the phosphate coating divided by the metal loss (both in mg/ft2). The article “Statistical Process Control of a Phosphate Coating Line” (Wire J. Intl., May 1997: 78–81) gave the accompanying data on tank temperature (x) and efficiency ratio (y).Temp. 170 172 173 174 174 175 176Ratio .84 1.31 1.42 1.03 1.07 1.08 1.04Temp. 177 180 180 180 180 180 181Ratio 1.80 1.45 1.60 1.61 2.13 2.15 .84Temp. 181 182 182 182 182 184 184Ratio 1.43 .90 1.81 1.94 2.68 1.49 2.52Temp. 185 186 188Ratio 3.00 1.87 3.08a. Construct stem-and-leaf displays of both temperature and efficiency ratio, and comment on interesting features.b. Is the value of efficiency ratio completely and uniquely determined by tank temperature? Explain your reasoning.c. Construct a scatterplot of the data. Does it appear that efficiency ratio could be very well predicted by the value of temperature? Explain your reasoning.he accompanying data on calcium content of wheat are consistent with summary quantities that appeared in a research article on how mineral contents of cereal grains were affected by storage and insect infestation. Four different storage times were considered. Storage Time Observations 0 months 58.75 57.94 58.91 56.85 55.21 57.30 1 month 58.86 56.42 56.51 57.67 59.75 58.48 2 months 59.12 60.39 58.01 59.95 59.51 60.34 4 months 62.33 58.76 60.02 59.36 59.61 61.95 Do these data provide evidence that the means for calcium content are not all the same for the four storage periods? Use the three-read strategy to understand the problem, and then test the relevant hypotheses using a significance level of 0.01. (Let ?1, ?2, ?3, and ?4 be the true mean calcium content for 0 months storage, 1 month storage, 2 months storage, and 4 months storage, respectively.) Find the test statistic. (Round your answer to two decimal places.) F =
- A deficiency of the trace element selenium in the diet can negatively impact growth, immunity, muscle and neuromuscular function, and fertility. The introduction of selenium supplements to dairy cows is justified when pastures have low selenium levels. Authors of the article “Effects of Short-Term Supplementation with Selenised Yeast on Milk Production and Composition of Lactating Cows” (Australian J. of Dairy Tech., 2004: 199–203) supplied the following data on milk selenium concentration (mg/L) for a sample of cows given a selenium supplement and a control sample given no supplement, both initially and after a 9-day period. Obs Init Se Init Cont Final Se Final Cont 1 11.4 9.1 138.3 9.3 2 9.6 8.7 104 8.8 3 10.1 9.7 96.4 8.8 4 8.5 10.8 89 10.1 5 10.3 10.9 88 9.6 6 10.6 10.6 103.8 8.6 7 11.8 10.1 147.3 10.4 8 9.8 12.3 97.1 12.4 9 10.9 8.8 172.6 9.3 10 10.3…rofessor Cornish studied rainfall cycles and sunspot cycles. (Reference: Australian Journal of Physics, Vol. 7, pp. 334-346.) Part of the data include amount of rain (in mm) for 6-day intervals. The following data give rain amounts for consecutive 6-day intervals at Adelaide, South Australia. 7 28 7 1 69 3 1 4 22 7 16 4 54 160 60 73 27 3 3 1 7 144 107 4 91 44 1 8 4 22 4 59 116 52 4 155 42 24 11 43 3 24 19 74 26 63 110 39 34 71 52 39 8 0 15 2 14 9 1 2 4 9 6 10 (i) Find the median. (Use 1 decimal place.)(ii) Convert this sequence of numbers to a sequence of symbols A and B, where A indicates a value above the median and B a value below the median. Test the sequence for randomness about the median at the 5% level of significance. (b) Find the number of runs R, n1, and n2. Let n1 = number of values above the median and n2 = number of values below the median. R n1 n2 (c) In the case, n1 > 20, we cannot use Table 10 of Appendix II to find the critical…Lyme disease is an inflammatory disease that results in a skin rash and flulike symptoms. It is transmitted through the bite of an infected deer tick. The following data represent the number of reported cases of Lyme disease and the number of drowning deaths for a rural county. Cases_of_Lyme_Disease Drowning_Deaths Month3 0 J2 1 F2 2 M4 1 A5 3 M15 9 J22 17 J13 5 A6 3…
