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- Estimate MSE of variance for x and YSuppose that 90% of Narnians are children, that Narnian children have normally distributed BMIs with a mean of 25 kg/m^2 and variance of 64 (kg/m^2)^2 , and that Narnian adults have normally distributed BMIs with a mean of 30 kg/m^2 and variance of 100 (kg/m^2)^2 . WHO currently categorizes BMIs greater than 30 as obese. a. What is the prevalence of obesity among Narnian children? b. What is the prevalence of obesity among Narnian adults? c. What is the overall prevalence of obesity among Narnians? d. Are age and obesity statistically independent in Narnia? e. What proportion of Narnians are obese children? f. What proportion of obese Narnians are children?Suppose that average male weight in the US is 175 pounds with a standarddeviation of 25 pounds. Suppose you randomly select 1,000 male Americans and ask their weight, and average the 1,000 numbers to compute a sample mean Xn. What is the variance of the sample mean Xn?
- A lot of 75 washers contains 6 defectives whose variability in thickness is unacceptably large. A sample of 10 washers is selected at random without replacement. a. Calculate the variance of (x)Assume that the population consists of only these eleven data points for y and z. Construct one sample for y and one another sample for z by using 5 data points which gives the maximum variance.If you still have some time, you can add your reviews about the contribution of Bessel’s Correction to the variance. Why do we use such correction and can the variance of any possible sample be larger than the variance of the population?2. The average zone of inhibition (in mm) for mouthwash L as tested by the medical technology students has been known to be 9mm. A random sample of 10 mouthwash L was tested and the test yielded an average zone of inhibition of 7.5mm with a variance of 25 mm. Is there enough reason to believe that the anti-bacterial property of the mouthwash has decreased? Test the hypothesis that the average zone of inhibition of the mouthwash is no less than 9mm using 0.05 level of significance. A. State the hypotheses. B. Determine the test statistic to use. C. Determine the level of significance, critical value, and the decision rule. D. Compute the value of the test statistic. E. Make a decision. F. Draw a conclusion.
- The data shown in the table represent the measurements of 10-kΩ resistors (in kΩ) produced from five different machines. A random sample of nine resistors from each machine is taken to determine whether the mean resistance varies from one machine to another. Perform analysis of variance and test the hypothesis at the 0.05 level of significance that the mean resistances differ significantly for the five machines, all through manual computations. Show all complete and systematic solutions.A study was conducted to compare the length of time between men and women to assemble a certain product. Sample standard deviation in a random sample of times for 11 men was 8.6 minutes, and sample standard deviation in a random sample of times for 13 women was 6.9 minutes. Past experience indicate that population of times is normal for both men and women. Is it sufficient sample evidence to conclude that the variance of the lengths of time for men is larger than the variance of the lengths of time for women? Test appropriate hypothesis at a = 0.05 level of significance using critical value approach. Use S²/S2 as test statistic. Construct a 90% confidence interval for the ratio of two population variances. a. State null and research hypotheses H: H₁ b. The observed value of test statistic is c. State the rejection region d. Insert the word sufficient or insufficient into the following statement. There is of time for men is larger than the variance of the lengths of time for women.…A simple random sample without replacement was used to select 5 clusters from a population of 29 clusters. From each selected sample cluster simple random sampling without replacement was used to select samples of secondary units. For this data find an estimate of the population total and the population mean along with their estimated variances. clmemb clsize yval [1,] [2,] [3,] [4,] [5,] [6,] [7,] [8,] [9,] [10,] [11,] [12,] [13,] [14,] [15,] [16,] [17,] [18,] [19,] [20,] [21,] [22,] [23,] [24,] [25,] [26,] [27,] [28,] [29,] [30,] [31,] [32,] [33,] 1 20 46.07 20 45.54 20 43.07 1 1. 1 20 49.29 1 20 44.35 1 20 45.21 2 33 44.11 2 33 42.19 2 33 44.42 2 33 40.05 2 33 43.88 2 33 47.45 2 33 40.41 2 33 43.24 3 22 35.42 3 22 35.46 3 22 36.34 3 22 35.25 4 40 38.67 4 40 34.73 4 40 39.28 4 40 35.26 4 40 39.84 4 40 40.32 4 40 40.03 4 40 38.15 4 40 38.69 4 40 39.38 18 47.48 18 44.78 5 18 44.37 18 44.97 5 18 49.20
- Last school year, the student body of a local university consisted of 35% freshmen, 25% sophomores, 24% juniors, and 16% seniors. A sample of 300 students taken from this year's student body was taken to determine if there had been a significant change in % of students for each classification for this year as compared to last year. This analysis is an example of a Regression O Goodness of Fit Analysis of Variance Test of Independence3 Suppose the following model yi=β1+ui Where ui is assumed to be normally distributed with mean zero and variance σ^2. Calculate analytically, following OLS technique, βHAT1and Var(βHAT1)Suppose that hemoglobin levels in white males over age 11 are normally distributed with variance 1.462 and that those for white males age 11 or under are normally distributed with variance 0.867. Independent random samples of 10 older and 20 younger white males are selected and produce sample means of 13.47 g per 100 ml and 12.64 g per 100 ml, respectively. Do the data indicate that older white males have higher hemoglobin levels than younger white males? Use a 0.01 level of significance.