6.A school desires to estimate the average score that would be obtained on a readingcomprehension exam for students in the sixth grade. The school has students divided into threetracks, with the fast learners in track I and the slow learners in track III. It was decided to stratifyon tracks since this method should reduce variability of test scores. The sixth grade contains 551students in track I, 80 in track II, and 65 in track III. A stratified random sample of 50 students isproportionally allocated and yields simple random samples of n₁ = 14, n₂ = 20, y n3 = 16 fromtracks I, II, and III, respectively. The test is administered to the sample of students with thefollowing results:Track I80687285906261Track II928587 5391817983854810965497253687159253K8TENG7573786981596142Track III654349854261423231291914313032Estimate the average score for the sixth grade, and place a bound on the error of estimation.Answer: Mean = 59.99; Error = 3.032 7. Suppose the average test score for the class in Exercise 6 is to be estimated again at the end ofthe school year. The cost of sampling are equal in all strata, but the variances differ. Find theoptimum (Neyman) allocation of a sample of size 50 using the data in Exercise 6 to approximatethe variances.Answer: n₁ = 11; n₂ = 21; n₂ = 188. Using the data in Exercise 6, find the sample size required to estimate the average score with abound of 4 points on the error of estimation. Use proportional allocation.Answer: n = 339. Repeat Exercise 8 using Neyman allocation. Compare the result with the answer to Exercise 8.Answer: n = 32

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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In a study comparing banks in two countries, a sample of 142 matched pairs of banks was formed. Each pair contained one bank from country x and one from country y. The pairings were made in such a way that the two members were as similar as possible in regard to such factors as size and age. The ratio of total loans outstanding to total assets was calculated for each of the banks. For this ratio, the sample mean difference (country x - country y) was 0.0579, and the sample standard deviation of the differences was 0.3086. Test, against a two-sided alternative, the null hypothesis that the two population means are equal. (Assume α = 0.01.) Click the icon to view the critical values of the Student's t distribution. The test statistic is t = 2.236. (Round to three decimal places as needed.) The critical value(s) is(are) (Round to three decimal places as needed. Use a comma to separate answers as needed.)
5. Use the data set 1. This is the result of a randomized trial in Uganda where 10 students in the same village were selected and given a solar-powered reading lamp. The second group was not given any lamp. The number of students out of 10 who improved their school grades for both groups were recorded. The experiment was repeated in 50 villages. Test the hypothesis that solar-powered reading lamps are effective in improving school grades in Uganda.
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6. A study of report writing by psychologist is conducted. A scale that measures the intelligibility of psychologist English is devised. This scale, called an "index of confusion" is devised so that low scores indicate high readability. These data are obtained on articles randomly selected from psychology journals and from unpublished reports written in 2015. Unpublished reports 2.39 Journals 1.79 1.75 1.67 1.65 2.51 2.86 2.14 1.87 1.75 1.94 2.56 2.29 2.49 1.62 2.06 1.33 2.36 2.58 2.33 1.96 1.69 1.70 2.62 2.41 1.94 a. Test the appropriate hypotheses. b. Does there appear to be a difference between u, and u, ? Explain.

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