4.2.9. Let X₁, X2,..., X9 be a random sample of size 9 from a distribution that isN(μ, 0²).(a) Ifo is known, find the length of a 95% confidence interval foris based on the random variable √9(X -μ)/o.flif this interval(b) Ifo is unknown, find the expected value of the length of a 95% confidenceif this interval is based on the random variable √9(x-μ)/S.Hint: Write E(S) = (o/√n - 1)E[((n − 1)S²/0²)¹/2].interval forfl(c) Compare these two answers.

Given: Let X1, X2,.....X9 be a random sample of size 9 from a distribution that is Normal with mean…

Answered: 4.2.9. Let X₁, X2,..., X9 be a random…

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 population is distributed with a known standard deviation, σ = 18 units. A random sample of size 35 is obtained from this population. The mean of this sample is 70. True or False: Since the sample size is greater than 25 the distribution of sample means from this population should be approximately normally distributed. What is the lower limit of the 95% confidence interval for the population mean μ? (2 dp) What is the upper limit of the 95% confidence interval for the population mean μ? (2 dp). Based on your confidence interval, would you believe that the true mean of this population could be 75?
(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
Let X1, X2, *. Xn be a random sample of size n from norm population with mean and unknown a. Let X and s be the sample mean and sample standard deviation. Then for any 0
Use the t-distribution and the given sample results to complete the test of the given hypotheses. Assume the results come from random samples, and if the sample sizes are small, assume the underlying distributions are relatively normal. Test Ho : HA = Ha VS H. : HA # Hg using the fact that Group A has 8 cases with a mean of 125 and a standard deviation of 18 while Group B has 15 cases with a mean of 118 and a standard deviation of 14. (a) Give the test statistic and thep-value. Round your answer for the test statistic to two decimal places and your answer for the p- value to three decimal places. test statistic = p-value = eTextbook and Media (b) What is the conclusion of the test? Test at a 10% level. O Reject Ho. O Do not reject Ho. eTextbook and Media
Q2: Let x1,X2, . , Xn and y1, y2, ..., Ym represent two independent random samples from the respective normal distributions N(H1,07) and N (H2, 03). It is given that of = 30, but ožis unknown. Then 1. A random variable that can be used to find a 95% confidence interval for - is (x- y) - (H1 - H2) А. ns3 + ms n+m. 3(n+m-2)"tm, nm O A (x – y) – (41 – H2) В. ns? + ms; n + m. (n + m – - 2) пт (x – y) – (41 - H2) С. ns3 + mS;_n+3 3(n+ m-2) ("+3m nm Ос
I need help with this one, please. I need it to be step-by-step please for me to understand.
This column contains data x1, . . . , xn, which is assumed to be a sample from a normal distribution N(µ, σ 2 ). For this sample, find the maximum likelihood estimates µˆ and σˆ.
Assume we have a sample of size n=16 from independent and identically distributed random variables from a normal distribution with mean u and unknwo standard deviation estimated by the sample standard deviation. We observe x =8 and s=4. We let e denote the length of the confidence interval with confidence level 1-a=95%. Which of the following statements are true? > qnorm(c (0.8,0.9,0.95,0.975,0.99,0.999)) [1] 0.8416212 1.2815516 1.6448536 1.9599640 2.3263479 3.0902323 > qt(c(0.8,0.9,0.95,0.975,0.99,0.999), df=15) [1] 0.866245 1.340606 1.753050 2.131450 2.602480 3.732834 Veuillez choisir au moins une réponse: O a. The confidence interval equals [6.25,9.75]. O b. The confidence interval equals [5.87,10.13]. The confidence interval equals [6.36,9.64]. O c. O d. The confidence interval equals [6.04,9.96].
Q2
If continuous random variable normally distributed with mu = 256.43 and J = 27.11 , what is P(225.75 <= x <= 300.35) ?
Let X equal the length of life of a 60-watt light bulb marketed by a certain manufacturer. We do not know the distribution of X except that Var(X) = 1158. Let u be the mean of X. Suppose a random sample of n = 25 bulbs is tested until they burn out, yielding a sample mean of = 1368 hours. (i) Compute an approximate 95% confidence interval for u. (ii) Compute an approximate 95% one-sided confidence interval for that provides a lower bound for u, i.e. compute & such that ɛ P(X - ≤ μµ)≈ 0.95.
Assume that a random variable Y has a mean of zero and standard deviation of one. Calculate the expected value of X1 and X2 if they are defined as below. X1 = Sigma+ Mu X2 = Sigma(Y+Mu)

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