Question 7,8,9 and 10 are related questions.Q7. A Random Variable X has an unknown distribution, a known mean of 10and an unknown variance, o. To test a claim that the distribution is nolonger 10, a random sample of 100 of X was collected which gave asample mean, x of 9.8 and a sample variance, s = 16.Which of these is the appropriate Null and Alternative hypothesis?A. Η6 μ- 10 ; H: μ 10.Β. Hg: μ- 10 ; Η: μ 10.C. Η: μ= 10 ; Η: μ > 10.D. x = 10 ; H1: X+ 10.||ОА. АОВ. ВО С. СO D. D

The claim is that the distribution is no longer 10.

Answered: Q7. A Random Variable X has an unknown…

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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Two independent samples have been selected, 7777 observations from population 1 and 5858 observations from population 2. The sample means have been calculated to be ?⎯⎯⎯1=13.4x¯1=13.4 and ?⎯⎯⎯2=11.3x¯2=11.3. From previous experience with these populations, it is known that the variances are ?21=27σ12=27 and ?22=29σ22=29. For the hypothesis test of ?0:(?1−?2)=1.8H0:(μ1−μ2)=1.8 and ??:(?1−?2)≠1.8Ha:(μ1−μ2)≠1.8 Use ?=0.04α=0.04. (a) Compute the test statistic. ?=z= (b) Find the approximate p-value?−?????=p−value= The final conclustion is A. There is not sufficient evidence to reject the null hypothesis that (?1−?2)=1.8(μ1−μ2)=1.8. B. We can reject the null hypothesis that (?1−?2)=1.8(μ1−μ2)=1.8 and accept that (?1−?2)≠1.8(μ1−μ2)≠1.8.
5.STATISTICAL INFERENCE
D.1.2 Test the hypothesis that the average content of containers of a particular lubricant is 10 liters if the contents of a random sample of 10 containers are 10.2, 9.7, 10.1, 10.3, 10.1, 9.8, 9.9, 10.4, 10.13, and 9.8 liters. Use α 0.01 level of significance and assume that the distribution of contents is normal.
Assume the random variable X has a standard deviation of 4, the random variable Y has a standard deviation of 5 and the two random variables have a correlation of 0.6. What is the covariance of X and Y?
1. Suppose a X value is produced by a random process that has a mean of 1 and a variance of 9, while a Y value is produced by a random process that has a mean of 9 and a variance of 1. Let Z = 3X - 2Y. Compute: a. the mean and variance of Z assuming X and X are independent. b. the mean and variance of Z assuming X and X are not independent and their correlation coefficient is 0.50.
3.3.24. Let X1, X2 be two independent random variables having gamma distribu- tions with parameters a₁ = 3, B₁ = 3 and a2 = 5, B2 = 1, respectively. (a) Find the mgf of Y = 2X₁ +6X2. (b) What is the distribution of Y?
Let X-1: correct, X=0 : wrong And P= Pr(X=1)=2/5 What is the variance? .32 O.6 O .4
Suppose that x and y are unknowns with ?(?)=E(X)= 11, var(?)=Var(X)=4, ?(?)=E(Y)= 7 and var(?)=Var(Y)= 100. In addition, suppose that the correlation coefficient of ?Xwith ?Yis .6. Then what is the expected value of xy?
9. Let 7 = 1.135013 be the sample mean of an iid sample r1,..., T50 from a gamma population Gamma(1, 3). Here ß > 0 is the unknown paramcter of interest. Construct an approximate 95%-CI for ß.
3.An insurance company employs agents on a commission basis. It claims that in their first year, agents will earn a mean of at least 40.000TL and that the population standard deviation is no more than 6.00OTL. A random sample of 9 agents are found for commissions in the first year and has values as follows: 9. 9. X; = 333000 ve (Xi – x)2 = 312000 i=1 i=1 Where x; are the values for each agent and the distribution is normal. a.Test at the 0.05 significance level the null hypothesis that the population mean is at least 40.000TL and interpret the result b.Test at 0.10 significance level the null hypothesis that the population standard deviation is at most 6.000TL and interpret the result.
12. Two independent samples are taken from two populations. Sample 1 has a mean of 12.8, a standard deviation of 2.3, and a sample size of 18. Sample 2 has a mean of 14.2, a standard deviation of 5.2, and a sample size of 23. This gives a standard error se(Ã1 — Ă2) = 1.212. A 95% confidence interval for the difference between the two means is: (A) (-2.00, -0.80). (B) (11.66, 13.94). (C) (-3.96, 1.16). (D) (-3.85, 1.05). (E) (-3.78, 0.98).
A sample of n = 7 scores is selected from a population with an unknown mean ( µ). The sample has a mean of M = 40 and a variance of s 2 = 63. Which of the following is the correct 95% confidence interval for µ?

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