Illustration 9.28. Comment on the performance of the students University Course of % of No.of students % of No.of students % of No.of students study Bombay Calcutta Madras pass in hundreds pass in hundreds pass in hundreds М.A. М.Com. 71 3 82 2 81 83 4 76 76 3.5 B.A. B.Com. 73 5 13 76 74 4.5 74 2 58 2 B. Sc. 65 3 65 70 7 M. Sc. 66 3 60 73 2 2 36 37
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- A dietitian wishes to see if a person’s cholesterol level will be changed if the diet is supplemented by a certain mineral. Four subjects were pre-tested, and they took the mineral supplement for a 6-week period. The results are shown in the table. Is there sufficient evidence to conclude that the population mean of cholesterol levels has been changed after six weeks at α=0.2α=0.2? Assume that the differences are from an approximately normally distributed population. Subject Cholestrol Level (mg/dl) Cholestrol Level after 6 Weeks (mg/dl) dd ¯dd¯ (d−¯d)2(d-d¯)2 1 206 217 11 2 219 184 -35 3 202 204 2 4 213 205 -8 Total -30 a) Calculate the mean, the sum of the squared deviation from the mean, and the standard deviation of differences. Do not include the unit for each answer: ¯d=d¯= (do not round) ∑(d−¯d)2=∑(d-d¯)2= (do not round) sd=sd= (rounded to one decimal place) b) Perform the hypothesis test in the following steps: Step 1.…An urban community wants to show that the incidence of breast cancer is higher in their locality than in a neighboring rural area. (PCB levels were found to be higher in the soil of the urban community). If you find that in the urban community 20 out of 200 adult women have breast cancer and that in the rural community 10 out of 150 adult women have it, could you conclude, at a significance level of 0.05, that breast cancer is more prevalent in the urban community?1. The parameter of interest is:2. The hypotheses for this test are:3. The calculated test statistic is:4. The critical region is:5. Draw the critical region (make decision):6. It can be concluded that:A pharmcuticle company claims that its new drug reduces systolic blood pressure. The systolic blood pressure (in millimeters of Mercury) for 9 patients before taking the new drug and 2 hours after taking the drug are shown in the table below. is there enough evidence support the company's claim? Let D =(blood pressure before taking new drug)- (blood pressure after taking new drug).use significant levels of a=their 0.05 for the test. Assume that the systolic blood pressure levels are normally distributed for the population of patience both Before & After taking the new drug. 1.State the null and alternative hypothesis for the test. 2. Find the value of the standard deviation of the paired differences. Round to one decimal place. 3.compute the value of the test statistic. Round to three decimal places 4.determine the decision rule for rejecting the null hypothesis Ho. Round the numerical portion to three decimals. 5.make decision for the hypothesis test.
- Compute the sum-of-squares error (SSE) by hand for the given set of data and linear model. (8, 10), (9, 11), (16, 20), (12, 2); y = 2x − 8The 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…Test the hypothesis that the average weekly allowance of female and male ACC 215 students the same, at 5%l evel of significance. Weekly Allowance of Students (Php) Male: 1500 2000 2500 2500 2000 1750 2000 1800 Female:1500 2000 1750 1500 2000 2500 3000 3500 Ho: Ha: α = Decision Rule: Computation: Decision: Conclusion:
- The article “Effect of Varying Solids Concentration and Organic Loading on the Performance of Temperature Phased Anaerobic Digestion Process” (S. Vandenburgh and T. Ellis, Water Environment Research, 2002:142–148) discusses experiments to determine the effect of the solids concentration on the performance of treatment methods for wastewater sludge. In the first experiment, the concentration of solids (in g/L) was 43.94 ± 1.18. In the second experiment, which was independent of the first, the concentration was 48.66 ± 1.76. Estimate the difference in the concentration between the two experiments, and find the uncertainty in the estimate.A local group of economists wants to study the effects of the pandemic on the small businesses in their city. A survey was sent out to a random sample of small businesses to anonymously report both their weekly earnings in $1000 for January 2020 (group 1) and January 2021 (group 2). Assume that the weekly earnings are normally distributed. Only 10 businesses provided enough data to compute their average weekly earnings for two months. The groups are dependent. Use α = 0.01 to decide whether there is sufficient evidence that the pandemic reduced the average weekly earnings for small businesses. January 2020 January 2021 58.2 60.5 78.3 62.5 38.2 40.9 32.7 36.2 43.8 36.2 33.7 30.9 50.5 41.4 56.3 38.3 41.1 37.9 26.4 21.7 1. What are the correct hypotheses? H0: H1: 2. Based on the hypotheses, compute the following: Round answers to at least 4 decimal places. The test statistic is = The critical value is =…A local group of economists wants to study the effects of the pandemic on the small businesses in their city. A survey was sent out to a random sample of small businesses to anonymously report both their weekly earnings in $1000 for January 2020 (group 1) and January 2021 (group 2). Assume that the weekly earnings are normally distributed. Only 10 businesses provided enough data to compute their average weekly earnings for two months. The groups are dependent. Use α = 0.01 to decide whether there is sufficient evidence that the pandemic reduced the average weekly earnings for small businesses. January 2020 January 2021 58.5 29.7 37.1 50.8 48.4 36.8 44.8 33.9 72.9 36.5 27.9 45.6 78.5 58.4 53.4 51.2 83.4 47 48.2 33.6 1) What are the correct hypotheses? H0: H1: 2) Based on the hypotheses, compute the following: Round answers to at least 4 decimal places. The test statistic is = The critical value is =…
