The article "Variance Reduction Techniques: Experimental Comparison and Analysis for Single Systems" (I. Sabuncuoglu, M. Fadiloglu, and S. Çelik, IIE Transactions, 2008:538–551) describes a study of methods for reducing variance in estimators of the mean inventory on hand. Two systems, the serial line system and the inventory system, were studied, along with two schemes for proportional sampling. The results given below (in percent) are consistent with the means and standard deviations reported in the article.
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- What is meant by the sample space of an experiment?The article “Variance Reduction Techniques: Experimental Comparison and Analysis for Single Systems” (I. Sabuncuoglu, M. Fadiloglu, and S. Çelik, IIE Transactions, 2008:538–551) describes a study of methods for reducing variance in estimators of the mean inventory on hand. Two systems, the serial line system and the inventory system, were studied, along with two schemes for proportional sampling. The results given below (in percent) are consistent with the means and standard deviations reported in the article. System Scheme Reduction Serial Line A 6.4 5.8 5.1 8.4 7.0 8.4 8.5 7.5 7.0 7.9 Serial Line B 4.7 4.7 3.8 5.3 10.6 4.5 8.2 10.8 5.1 5.7 Inventory A 11.0 8.9 9.3 9.2 7.9 9.7 9.0 12.5 6.7 9.8 Inventory B 8.9 7.0 10.7 10.3 6.2 12.2 7.0 9.5 8.7 9.7 PLEASE USE EXCEL Construct an ANOVA table. You may give ranges for the P-values. 2. Is the additive model…NutritionResearchers compared protein intake among threegroups of postmenopausal women: (1) women eating astandard American diet (STD), (2) women eating a lactoovo-vegetarian diet (LAC), and (3) women eating a strictvegetarian diet (VEG). The mean ± 1 sd for protein intake(mg) is presented in Table 12.29. 12.5 Using the data in Table 12.29, perform a multiplecomparisons procedure to identify which specific underlyingmeans are different.
- The Occupational Safety and Health Administration (OSHA) mandates certain regulations that have to be adopted by corporations. Prior to the implementation of the OSHA program, a company found that for a sample of 40 randomly selected months, the mean employee time lost due to job-related accidents was 45 hours. After implementation of the OSHA program, for a random sample of 45 months, the mean employee time lost due to job-related accidents was 39 hours. It can be assumed that the variability of time lost due to accidents is about the same before and after implementation of the OSHA program (with a standard deviation being 3.5 hours). Find a 90% confidence interval for the difference in the mean time lost due to accidents. Test the hypothesis that implementation of the OSHA program has reduced the mean employee lost time. Use a level of significance of 0.10.To compare customer satisfaction levels of two competing ice cream companies, 8customers of Company 1 and 5 customers of Company 2 ware randomly selectedand were asked to rate their ice creams on a five-point scale, with 1 being leastsatisfied and 5 most satisfied. The survey results are summarized in the followingtable:Company 1 Company 2?1=8 ?2=5?1̅̅̅̅=3.21 ?2̅̅̅̅=2.22?1= 0.31 ?2= 0. 21By assuming both equal variances and unequal variances:a. Construct an interval estimate at 95°/ confidence interval for difference of means of two ice cream companies..In testing for the equality of two population variances, when the populations are normally distributed, the 10% level of significance has been used. Determine the upper-tail area of rejection region.
- The marketing manager of a large super-market chain has the business objective of using shelf space most efficiently. Toward that goal, they would like to use shelf space to predict the sales of a specialty pet food. Data are collected from a random sample of 12 equal-sized store, with the following results: Shelf Space Sales Aisle Location 5 160 0 5 220 1 5 140 0 10 190 0 10 240 0 10 260 1 15 230 0 15 270 0 15 280 1 20 260 0 20 290 0 20 310 1 For these data, Syx = 30.8058436 and hi = 0.1373333 when X = 8. *Round final answers below to three decimal places. Do not round calculations until the final answer. (a) Construct a 95% confidence interval estimate of the mean weekly sales for all stores that have 8 square feet of shelf space for pet food. (b) Construct a 95% prediction interval of the weekly sales of an individual store that has 8 square feet of shelf…A corporation is trying to decide which of three makes of automobile to order for its fleet—domestic, Japanese, or European. Five cars of each type were ordered, and, after 10,000 miles of driving, the operating cost per mile of each was assessed. The accompanying results in cents per mile were obtained. Domestic Japanese European 18.0 20.1 19.3 15.6 15.6 15.4 15.4 16.1 15.1 19.1 15.3 18.6 16.9 15.4 16.1 a. Prepare the analysis of variance table for these data. b. Test the null hypothesis that the population mean operating costs per mile are the same for these three types of car. c. Compute the minimum significant difference and indicate which subgroups have different means.A study, which randomly surveyed 3,700 households and drew on this information from the IRS, found that 79% of households have conducted at least one IRA rollover from an employer-sponsored retirement plan. Suppose a recent random sample of 90 households in a certain county was taken and respondents were asked whether they had ever funded an IRA account with a rollover from an employer-sponsored retirement plan. Based on the sample data below, can you conclude at the 0.10 level of significance that the proportion of households in the county that have funded an IRA with a rollover is different from the proportion for all households reported in the study? 77 respondents said they had funded an account; 13 respondents said they had not
- A researcher was interested in comparing the salaries of female and male employees at a particular company. Independent simple random samples of 8 female employees and 15 male employees yielded the following weekly salaries (in dollars). Female Male 495 722 518 760 562 904 556 880 1150 904 520 805 520 500 480 1005 1250 970 743 750 605 660 1640 Use a 0.01 significance level to test the claim that the mean salary of female employees is less than the mean salary of male employees.The sales price (in $1,000) of three-bedroom apartments in two cities—Houston, Texas, and Orlando, Florida—are given in the following table. Houston is known to have lower house prices than Orlando; however, it is not clear if it also has lesser variability in its prices. Houston 189 145 220 205 225 275 248 310 150 318 Orlando 301 279 224 400 249 205 289 350 218 300 State the null and the alternative hypotheses to determine if the variance of house price in Houston is less than that in Orlando. What assumption regarding the population is necessary to implement this step? Test the hypothesis at α = 0.05. What is your conclusion?. Although there is a popular belief that herbal remedies such as Ginkgo biloba and Ginseng may improve learning and memory in healthy adults, these effects are usually not supported by wellcontrolled research (Persson, Bringlov, Nilsson, and Nyberg, 2004). In a typical study, a researcher obtains a sample of n = 16 participants and has each person take the herbal supplements every day for 90 days. At the end of the 90 days, each person takes a standardized memory test. For the general population, scores from the test form a normal distribution with a mean of μ = 50 and a standard deviation of σ = 12. The sample of research participants had an average of M = 54. Assuming a two-tailed test, state the null hypothesis in a sentence that includes the two variables being examined. Using the standard 4-step procedure, conduct a two-tailed hypothesis test with α = .05 to evaluate the effect of the supplements.