Let S and S denote the variances of random samples, of sizes n and m respectively, fromtwo independent distributions which are N(u1,02) and N(u2, 02), respectively. Note thatthe two populations have different means but the same variances. You may use the fact thatnSỉ + mS?has the distribution x? with (n + m – 2) dfo2to help you to find a confidence interval for the common unknown variance o².

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Answered: Let S and S denote the variances of…

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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Let x represent the average annual salary of college and university professors (in thousands of dollars) in the United States. For all colleges and universities in the United States, the population variance of x is approximately o² = 47.1. However, a random sample of 17 colleges and universities in Kansas showed that x has a sample variance s² = 82.7. Use a 5% level of significance 1 test the claim that the variance for colleges and universities in Kansas is greater than 47.1. (a) What is the level of significance? State the null and alternate hypotheses. Ho: o²=47.1; H: o> 47.1 Ho: o²=47.1; H: o2 0.100 0.050 a, we fail to reject the null hypothesis. Since the P-value > x, we reject the null hypothesis. Since the P-values ∞, we reject the null hypothesis. Since the P-values a, we fail to reject the null hypothesis. (e) Interpret your conclusion in the context of the application. At the 5% level of significance, there is insufficient evidence to conclude the variance of annual salaries…
Suppose it is desired to estimate the variance of the tensile strength of a particular type of thread. For 21 pieces of this type of thread, E (X; – Xave)² = 2000. Suppose a hypothesis testing procedure is wished to be carried out to check whether or not it is safe to assume that the variability in tensile strength of thread is 110. Derive the condition that needs to be satisfied, expressed in terms of the value of s? (sample variance), such that the null hypothesis will be accepted. (Use 0.05 level of significance.) What is the maximum value of s? such that we still accept tensile strength variability to be 110?
What are the null hypothesis (H,) and the alternative hypothesis (H,) that should be used for the test? |Ho: µ is ? |H: µ is ? In the context of this test, what is a Type II error? V? v when, in A Type II error is ? fact, u is ? | the hypothesis that u is ? Suppose that the consultant decides not to reject the null hypothesis. What sort of error might she be making? ?
Find the approximate mean and variance of Y = √X, where X is a randomvariable following a Poisson distribution.
A taxi company is trying to decide whether to purchase brand A or brand B tires for its fleet of taxis. To estimate the difference in the two brands, an experiment is conducted using 14 of each brand. The tires are run until they wear out. The results are given in the table below. Compute a 90% confidence interval for μA−μB assuming the populations to be approximately normally distributed. You may not assume that the variances are equal. Brand A x1=35,300 kilometers s1=4900 kilometers Brand B x2=37,200 kilometers s2=6100 kilometers
In Company X, the personnel department gives two aptitude tests to applicants. One measures verbal ability while the other measures quantitative ability. From many years of experience, the company has found that a person's verbal score Y1 is normally distributed with mean of 50 and standard deviation (stdev) of 10. The quantitative scores Y2 are also normally distributed with mean of 100 and stdev 20. Y1 and Y2 appear to be independent. A composite score, Y, is assigned to each applicant where: Y= 3Y1 + 2Y2.Applicants whose composite scores are below 375 are automatically rejected. What is the probability that a random applicant gets automatically rejected? If six applicants submit resumes, what are the chances that fewer than half will fail the screening test?
The mean and variance of a binomial variate X are 4 and 4/3 respectively. Find P(X ≥ 3)
A random sample of size 225 is taken from a population with a mean of 10 and variance 4. Find the probability that the sample mean is greater than 9.8 but less than 10.2.
Executives of a supermarket chain are interested in the amount of time that customers spend in the stores during shopping trips. The mean shopping time, µ, spent by customers at the supermarkets has been reported to be 40 minutes, but executives hire a statistical consultant and ask her to determine whether it can be concluded that u is greater than 40 minutes. To perform her statistical test, the consultant collects a random sample of shopping times at the supermarkets. She computes the mean of these times to be 44 minutes and the standard deviation of the times to be 15 minutes. Based on this information, answer the questions below. What are the null hypothesis (H,) and the alternative hypothesis (H,) that should be used for the test? Hiµ is ? H: p is ? In the context of this test, what is a Type II error? A Type II error is ? fact, u is ? the hypothesis that u is when, in Suppose that the consultant decides not to reject the null hypothesis. What sort of error might she be making?

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