A factorial experiment was designed to determine factors in a high-energy electron beam process that affect hardness in metals. Results for two factors, each with three levels, are presented in the following ANOVA table. Factor A is the travel speed in mm/s, and factor B is accelerating voltage in volts. The outcome is Vickers hardness. There were six replications for each treatment.
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- 4.A new vitamin supplementation program is intended to decrease average resting heart rate inindividuals at risk for hypertension. Assume that a team of researchers are hopeful that restingheart rate in their population will get down to less than 68 bpm, in a population with a standarddeviation of 2 bpm. In order to test this goal reduction, the team gathers a SRS of 273participants in their program and calculates a sample average resting heart rate of 74 bpm.A) Carry out a one sample Z test to determine if the team can conclude that the supplementationprogram is successful in meeting their goal reduction in resting heart rate. Use an α=0.05.B) Construct a 95% Confidence interval about the sample mean, and interpret the result.1) A cement producer, manufactures and then fills 40kg-bags of powder cement on twodistinct production tracks located in separate suburbs. To determine whether differencesexist between the average fill rates for the two tracks, a random sample of 25 bags fromTrack 1 and a random sample of 16 bags from Track 2 were recently selected. Each bag’sweight was measured and the following information measures from the samples arereported:Production ProductionTrack 1 Track 2n1 = 25 n2 = 16x2 = 40.02 x1 = 39.87 s1 = 0.59 s2 = 0.88 Supervision believes that the fill rates of the two tracks are normally distributed with equalvariances.Construct a 95% confidence interval estimate of the true mean difference between the twotracks.--------------------------------------------------------------------------------------------------------------2) Two independent simple random samples were selected from two normallydistributed populations with unequal variances yielded the following information:Sample 1…1. The Federal Seed Act (FSA) dictates minimum germination standard for vegetable seed in interstate commerce (https://www.law.cornell.edu/cfr/text/7/201.31). The table at the link states that carrot seed must have a germination rate at least 55%. This means that if the seeds are planted under appropriate conditions, at least 55% of them will sprout.A producer of carrot seed would like to ensure their seeds exceed the standard. They take random samples of 1200 seeds and plant them under appropriate conditions. Of the 1200 seeds, 712 of them germinate. A. State the question of interest and parameter of interest. b. State the null and alternative hypotheses. c. Write down an inventory of the information given. d. Check the conditions needed for inference. There are two conditions. State each condition and whether it is met in this study. e. Calculate the test statistic. f. Calculate the p-value. (Drawing a picture is always helpful.) g. Write the conclusion in context.
- 2. Consider a study where students are measured on whether they had an internship during their time at WKU (Y/N) and whether they had a job at graduation (Y/N). If we wanted to test whether having an internship was associated with having a job at graduation (i.e., internship holders were more likely to have jobs), why would the chi-square test be inappropriate for this hypothesis? How should we analyze our data?7 How many degrees of freedom (df) are associated with two different samples, 15 participants in each sample for a study investigating the effects of illumination of productivity under two treatment conditions?8.7 It is conjectured that when fields are overgrazed by cattle there will be a substantial reduc- tion in the available grass during the subsequent grazing season due to the compaction of the soil. A horticulturist at the state agricultural experiment station designs a study to evaluate the conjec- ture. Twenty-one plots of land of nearly the same soil texture and suitable for grazing are selected for the study. Three grazing regimens selected for evaluation are randomly assigned to 7 plots each. After the 21 plots are subjected to the grazing regimens for four months, the researcher randomly selects 10 soil cores from each plot and measures the bulk density (g/cm3) in each soil core. The mean soil density of the 10 cores from each plot is given in the following table. Grazing Regimen Soil Denisty (g/cm3) Continuous grazing 2.05 3.05 3.12 1.59 3.83 1.53 1.44 Three-week grazing, one-week no grazing 1.20 1.48 3.54 1.03 1.45 1.40 2.68…
- Colonoscopy is a medical procedure that is designed to find and remove precancerous lesions in the colon before they become cancerous. The article “Association of Colonoscopy and Death from Colorectal Cancer” (N. Baxter, M. Goldwasser, et al., Annals of Internal Medicine, 2009:1–8) reports that in a sample of 10,292 people diagnosed with colorectal cancer, 7.0% had previously had a colonoscopy, and in a sample of 51,460 people without colorectal cancer, 9.8% had previously had a colonoscopy. Can you conclude that the percentage of people who have had colonoscopies is greater in those without colorectal cancer?2.Researchers studied selenium levels in beef raised in a low selenium region of the United States. The goal of the study was to compare selenium levels in the region-raised beef to selenium levels in cooked venison, squirrel, and beef from other regions of the United States. The data in the Excel file (se_level.xlsx or se_level.txt) are the selenium levels calculated on a dry weight basis in mg=100 g for a sample of 53 region-raised cattle 11.23 29.63 20.42 10.12 39.91 32.66 38.38 36.21 16.39 27.44 17.29 56.20 28.94 20.11 25.35 21.77 31.62 32.63 30.31 46.16 56.61 24.47 29.39 40.71 18.52 27.80 19.49 15.82 27.74 22.35 34.78 35.09 32.60 37.03 27.00 44.20 13.09 33.03 9.69 32.45 37.38 34.91 27.99 22.36 22.68 26.52 46.01 38.04 30.88 30.04 25.91 18.54 25.51 Please answer the following questions: Use these data to construct: A…2.Researchers studied selenium levels in beef raised in a low selenium region of the United States. The goal of the study was to compare selenium levels in the region-raised beef to selenium levels in cooked venison, squirrel, and beef from other regions of the United States. The data in the Excel file (se_level.xlsx or se_level.txt) are the selenium levels calculated on a dry weight basis in mg=100 g for a sample of 53 region-raised cattle 11.23 29.63 20.42 10.12 39.91 32.66 38.38 36.21 16.39 27.44 17.29 56.20 28.94 20.11 25.35 21.77 31.62 32.63 30.31 46.16 56.61 24.47 29.39 40.71 18.52 27.80 19.49 15.82 27.74 22.35 34.78 35.09 32.60 37.03 27.00 44.20 13.09 33.03 9.69 32.45 37.38 34.91 27.99 22.36 22.68 26.52 46.01 38.04 30.88 30.04 25.91 18.54 25.51 Please answer the following questions: Describe these data with…
- 7. The manufacturer of an Engine Energizer System (EES) claims that it improves gas mileage and reduces emissions in automobiles by using magnetic-free energy to increase the amount of oxygen in the fuel for greater combustion efficiency. Following are test results, performed under international and U.S. government agency standards, on a random sample of 14 vehicles. The data (also see file M09_Gas_Paired.txt or M09_Gas_Q7.xlsx) give the carbon monoxide (CO) levels, in parts per million, of each vehicle tested, both before installation of EES and after installation. (a)Test at the 1% significance level whether, on average, EES reduces CO emissions (b)Obtain a 99% confidence interval for the difference between the mean CO emissions before and after installation of EES corresponding to the test in part (a) (c)Interpret the confidence interval obtained in part (b). Does this interval support the conclusion of the hypothesis test in part (a)? Justify your answer9 What particular aspects of the SPSS output would you look at to make your decision about the best model?A recent study examined the effects of carbon monoxide exposure on a group of construction workers. The following table presents the numbers of workers who reported various symptoms, along with the shift (morning, evening, or night) that they worked. Morning Shift Evening Shift Night Shift Influenza 19 12 17 Headache 15 33 6 Weakness 12 14 7 Shortness of Breath 6 10 7 Send data to Excel Test the hypothesis of independence. Use the =α0.10 level of significance and the P-value method with the TI-84 Plus calculator. What do you conclude? H0: The shift and reported symptoms are/are not independent. H1: The shift and reported symptoms are/are not independent. This hypothesis test is a left tailed/right tailed/two tailed test.