In an experiment to compare bearing strengths of pegs inserted in two different types of mounts, a sample of 14 observations on stress limit for red oak mounts resulted in a sample
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Student Solutions Manual for Devore's Probability and Statistics for Engineering and the Sciences, 9th
- The article “Tibiofemoral Cartilage Thickness Distribution and its Correlation with Anthropometric Variables” (A. Connolly, D. FitzPatrick, et al., Journal of Engineering in Medicine, 2008:29–39) reports that in a sample of 11 men, the average volume of femoral cartilage (located in the knee) was 18.7 cm3 with a standard deviation of 3.3 cm3 and the average volume in a sample of 9 women was 11.2 cm3 with a standard deviation of 2.4 cm2. Find a 95% confidence interval for the difference in mean femoral cartilage volume between men and women.arrow_forward4) Your construction company has purchased two lots of southern yellow pine lumber, both supposedly with 4% moisture content. The mean perpendicular compression strength of the first lot is tested with a sample of n1 = 13 boards, yielding x = 14.8 MPa. A test of a sample of n2 = 13 boards from the second lot, which arrives after several days of rain and is wet, results in x, = 13.7 MPa. The population standard deviations are known to be the same, at of = ož = o? = 0.5 MPa. Complete the following: (a) Conduct a hypothesis test with a = 0.01 to see if the mean perpendicular compression strengths of the two populations are the same or not. Your work should show all 7 steps of the hypothesis testing procedure. On the cover sheet, just write your conclusion. (i.e., "There is/is not sufficient evidence at the a = 0.01 level of significance to conclude that the mean perpendicular compression strengths..") (b) For the results of your hypothesis test in part (a), what is the p-value for this…arrow_forwardAn experiment is performed to test the difference in effectiveness of two methods of cultivating wheat. A total of 12 patches of ground are treated with shallow plowing and 14 with deep plowing. The average yield per ground area of the shallow plowing group is 45.2 bushels, and the average yield for the deep plowing group is 48.6 bushels. Suppose it is known that shallow plowing results in a ground yield having a standard deviation of 0.8 bushels, while deep plowing results in a standard deviation of 1.0 bushels. At the 0.05 level of significance, a researcher wants to test the given data if it is consistent with the hypothesis that the mean yield is the same for both methods. What is the variable of interest of the study? Methods of cultivating wheat a. b. Types of wheat Number of patches per ground area of wheat C. d. Yield per ground area of wheatarrow_forward
- A researcher compares two compounds (1 and 2) used in the manufacture of car tires that are designed to reduce braking distances for SUVs equipped with the tires. SUVs equipped with tires using compound 1 have a mean braking distance of 7777 feet and a standard deviation of 12.812.8 feet. SUVs equipped with tires using compound 2 have a mean braking distance of 8585 feet and a standard deviation of 5.35.3 feet. Suppose that a sample of 3333 braking tests are performed for each compound. Using these results, test the claim that the braking distance for SUVs equipped with tires using compound 1 is shorter than the braking distance when compound 2 is used. Let μ1μ1 be the true mean braking distance corresponding to compound 1 and μ2μ2 be the true mean braking distance corresponding to compound 2. Use the 0.10.1 level of significance. Step 1 of 4 : State the null and alternative hypotheses for the test.arrow_forwardAn experiment was performed to compare the abrasive wear of two different laminatedmaterials. Twelve pieces of material 1 were tested by exposing each piece to a machine measuring wear.Ten pieces of material 2 were similarly tested. In each case, the depth of wear was observed. Thesamples of material 1 gave an average wear of 85 units with a sample standard deviation of 4, while thesamples of material 2 gave an average of 81 units and a sample standard deviation of 5. Can weconclude at the 0.05 level of significance that the abrasive wear of material 1 exceeds that of material 2by more than 2 units? Assume that the population to be approximately normal with potentially unequalvariances.arrow_forwardThe concentration of hexane (a common solvent) was measured in units of micrograms per liter for a simple random sample of nineteen specimens of untreated ground water taken near a municipal landfill. The sample mean was 289.2 with a sample standard deviation of 6.3. Twenty-two specimens of treated ground water had an average hexane concentration of 285.3 with a standard deviation of 7.6.It is reasonable to assume that both samples come from populations that are approximately normal. Can you conclude that the mean hexane concentration is less in treated water than in untreated water? Use the α = 0.10 level of significance. Use 6-step p-value method.arrow_forward
- An experiment was performed to compare the abrasive wear of two different laminated materials. Twelve pieces of material 1 were tested by exposing each piece to a machine measuring wear. Ten pieces of material 2 were similarly tested. In each case, the depth of wear was observed. The samples of material 1 gave an average (coded) wear of 85 units with a sample standard deviation of 4, while the samples of material 2 gave an average of 81 with a sample standard deviation of 5. Can we conclude at the 0.05 level of significance that the abrasive wear of material 1 exceeds that of material 2 by more than 2 units? Assume the populations to be approximately normal with equal variances.arrow_forwardConsider that an insurance actuary claims that the average footwell intrusions for small and medium cars is the same. Impact tests of 40 miles per hour were performed on 12 randomly selected small cars and 17 randomly selected medium cars. The average amount that the footwell bursts into the driver's legs has been measured. The average footwell intrusion in small cars was 10.1 cm with a standard deviation of 4.11 cm. For medium cars it was 8.3 cm with a standard deviation of 4.02 cm. Consider α = 0.10, and assume that the population variances are equal. Regarding the data presented, what decision making should be taken about the null hypothesis: We should: a) Reject the null hypothesis. b) Fail to Reject the Null Hypothesis.arrow_forward
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