(1)(2)Compare empirically the power of Shapiro-Wilk test and Kolmogrov-Samirnov test to test the normality of a set of data.Show empirically central limit theorem.Hint: Sample from different distributions and then thus test thedistribution of the sample mean. Thus obtain the empirical expectationof the sample mean and standard error.

Solution: According to the guidelines if multiple questions are asked only first question should be…

Answered: Compare empirically Samirnov test to…

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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A study tested the claim that heights of Americans and heights of Austrians have different variances with s=7.48092 cm for Americans and 7.14756 cm for Austrians. The sample sizes are n1= 145 and n2= 157. When using the F test with these data, is it correct to reason that there is no need to check for normalcy because n1 is greater than 30, and n2 is greater than 30?
A random of 15 freshmen takers obtained a mean score of 74 and a variance of 9 on a SASE. Assuming the scores to be normally distributed, construct a 95% confidence interval to estimate the variance of scores of the whole freshmen population.
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An instructor of statistics believes that the mean score of students on the first statistics test is 65 out of 100 marks. He randomly samples 10 statistics student scores and obtains the average scores as 63 with a standard deviation of 5.01. He performs a hypothesis test to know whether the mean score of students is varied from 65 by using a 5% level of significance.
Gestation period is the length of pregnancy, or to be more precise, the interval between fertilization and birth. In Syrian hamsters, the average gestation period is 16 days. Suppose you have a sample of 31 Syrian hamsters who were exposed to high levels of the hormone progesterone when they were pups, and who have an average gestation length of 17.1 days and a sample variance of 26.0 days. You want to test the hypothesis that Syrian hamsters who were exposed to high levels of the hormone progesterone when they were pups have a different gestation length than all Syrian hamsters. Calculate the t statistic. To do this, you first need to calculate the estimated standard error. The estimated standard error is sMM= a. 31, b. 0.5232, c. 0.7328, d. 0.9158. The t statistic is- a. 1.50, b. 2.10, c. 2.63, d. 1.20 Now suppose you have a larger sample size n = 95. Calculate the estimated standard error and the t statistic for this sample with the same sample average and the same…
A company produces bags of refined sugar. We are interested in testing the hypothesis that the average weight of the bags is 20 kg. The weights of the contents of these bags are normally distributed with a population variance of 1.96 square kg. The contents of a random sample of 49 bags had a mean weight of 19.7 kg. Then the value of the test statistic is اختر أحد الخيارات a. -1.50 b. 1.50 O C. 1.07 O d. -1.07 O
The life span of a certain wood cutting machine manufactured by a factory has a normal distribution with a guarantee that any machine that stars malfunctioning within 36 months of the purchase will be replaced by a new one. How many percentages of machines are expected to be replaced in the following cases? Mean of 60 months and variance of 64 months2 Mean of 45 months and variance of 36 months2 Mean of 75 months and variance of 16 months2
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What is the null hypothesis for a two-tailed test of Pearson's r correlation coefficient and how is it tested using a significance level of alpha=0.05?
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 researcher decides to measure anxiety in group of bullies and a group of bystanders using a 23-item, 3 point anxiety scale. Assume scores on the anxiety scales are normally distributed and the variance among the group of bullies and bystanders are the same. A group of 30 bullies scores an average of 21.5 with a sample standard deviation of 10 on the anxiety scale. A group of 27 bystanders scored an average of 25.8 with a sample standard deviation of 8 on the anxiety scale. You do not have any presupposed assumptions whether bullies or bystanders will be more anxious so you formulate the null and alternative hypothesis based on that.
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Compare empirically Samirnov test to test the normality the power of Shapiro-Wilk test and Kolmogrov- of a set of data.