= 20 is obtained from a18. A simple random sample of sizepopulation with μ = 64 and a = 17.(a) What must be true regarding the distribution of thepopulation in order to use the normal model to computeprobabilities involving the sample mean? Assuming that thcondition is true, describe the sampling distribution of i(b) Assuming that the requirements described in part (a) aresatisfied, determine P(x< 67.3).0.8078(c) Assuming that the requirements described in part (a) aresatisfied, determine P(x ≥ 65.2).0.3745(d) Compare the results obtained in parts (b) and (c) withthe results obtained in parts (b) and (c) in Problem 17What effect does increasing the sample size have on theprobabilities? Why do you think this is the case?

From the information, given thatLet X denotes the random variable with the population mean of 64 and…

Answered: 18. A simple random sample of size = 20…

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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(8)(1)
Suppose the random variable, X, follows a geometric distribution with parameter (0< 0 <1). Let X₁, X₂, X, be a random sample of size n from the population of X. (d) Find the method of moments estimator (mme) of 0. (e) Show how the mle of 0 is related to its mme. Explain if it is always true. (f) Verify if X, is a sufficient statistic for 8 or not. (g) Justify if = is an unbiased estimator for 6.
(e) Show that the sample mean of a simple random sample (drawn without replacement from a normal population) is dis- tributed normally with mean u and variance -² (1--=-1). n where N and n are population and sample sizes respectively. 4 In the 1 1 TI
Q2
A consumer group claims that the mean minimum time it takes for a sedan to travel a quarter mile is greater than 14.5 seconds. A random sample of 24 sedans has a mean minimum time to travel a quarter mile of 15.4 seconds and a standard deviation of 2.09 seconds. At α=0.01 is there enough evidence to support the consumer group's claim? Complete parts (a) through (d) below. Assume the population is normally distributed.
16. Let X, X2 X, be a random sample from a normal distribution, X, N(6, 25), and denote by X and S2 the sample mean and sample variance. Use tables from Appendix C to find each of the following: (a) P[3 < X < T. (b) P[L860< 3(X-6)/S]. (c) PIS <319375]
Exercise 1. Given a population with mean μ=400 and variance σ2 =1,600, the central limit theorem applies when the sample size is n>=25. A random sample of size n=35 is obtained. What is the variance of the sampling distribution of the sample means =6.7612 I dont understand why the answer for the question is (variance / 35 )^(1/2) and not 1600^(1/2)
A random sample of 10 observations from population A has sample mean of 152.3 and a sample standard deviation of 1.83. Another random sample of 8 observations from population B has a sample standard deviation of 1.94. Assuming equal variances in those two populations, a 99% confidence interval for μA − μB is (-0.19, 4.99), where μA is the mean in population A and μB is the mean in population B. (a) What is the sample mean of the observations from population B? (b) If we test H0 : μA ≤ μB against Ha : μA > μB, using α = 0.02, what is your conclusion?
A consumer group claims that the mean minimum time it takes for a sedan to travel a quarter mile is greater than 14.8 seconds. A random sample of 22 sedans has a mean minimum time to travel a quarter mile of 15.5 seconds and a standard deviation of 2.09 seconds. At α=0.01 is there enough evidence to support the consumer group's claim? Complete parts (a) through (d) below. Assume the population is normally distributed (a) Identify the claim and state H0 and Ha. b) THe claim is the _______ hypothesis. c) t= d) p= e) Decide whether to reject or fail to reject the null hypothesis. f) Interpret the decision in the context of the original claim.
The thickness (in millimeters) of the coating applied to hard drives is one characteristic that determines the usefulness of the product. When no unusual circumstances are present, the thickness (x) has a normal distribution with a mean of 3 mm and a standard deviation of 0.05 mm. Suppose that the process will be monitored by selecting a random sample of 16 drives from each shift's production and determining x, the mean coating thickness for the sample. (a) Describe the sampling distribution of x for a random sample of size 16. The distribution of x is with mean mm and standard deviation 0.0125 mm. (b) When no unusual circumstances are present, we expect x to be within 2? x of 3 mm, the desired value. An x value farther from 3 mm than 2? x is interpreted as an indication of a problem that needs attention. Calculate 3 ± 2? x. 3 − 2? x = mm 3 + 2? x = mm (c) Referring to part (b), what is the probability that a sample mean will be outside 3 ± 2? x just by chance…
a) Let X₁, X2, X3,..., X₁ be a random sample of size n from population X. Suppose that X follows an exponential distribution with parameter 0 and Y = ===1 X₁. n b) i) Show that y follows a chi-square distribution with 2n degrees of freedom. ii) What is the value of the sample size n, if P(Y > 20.4831) = 0.025? iii) What is the value of sample size n, if P(|Y - 2n| <40) ≥ 0.025? iv) Use the Central Limit Theorem to compute P(100 < Y < 115), for n = 40. Let X₁, X2, ..., X5 be a random sample of size 5 from the standard normally population. If the statistic Y is given by Y = X1 X2 X3 ₁²+X3² +X5² i) Briefly explain why Y follows a Student's t distribution with 3 degrees of freedom. ii) Compute the probability that Y is between 2.35 and 5.84. iii) What is the mean and variance of the statistic Y?

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