Suppose that X is a normal random variable with mean\( \mu = 50.1 \) and standard deviation \( \sigma = 10.4 \).Let \( \bar{X} \) denote the variable for the process of taking a random sample and calculating the sample mean (We called this the sampling distribution of the sample mean). Suppose that the sample size is 26. Calculate the standard deviation of the sampling distribution of the sample mean (also called standard error and denoted as \( \sigma_{\bar{X}} \) ). Enter your answer to three decimal places.

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Answered: Suppose that X is a normal 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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* Let X is a Gaussian random variable with zero mean an variance o. Y = X. Find mean of Random Variable Y.
An IQ test is designed so that the mean is 100 and the standard deviation is 10 for the population of normal adults. Find the sample size necessary to estimate the mean IQ score of statistics students such that it can be said with 99% confidence that the sample mean is within 8 IQ points of the true mean. Assume that σ=10 and determine the required sample size.
Let x be a random variable that represents the pH of CVS brand water. The mean of this x distribution is µ = 6.5 pH. A new company wants to sell its water at CVS locations. However, CVS management believes that the new brand will have a mean pH less than the CVS brand water. A random sample of 50 water samples were taken from this new company's water and it was found that the sample mean was 6.3 pH and the sample standard deviation was s = 0.5 pH. Do the data indicate that the new company's water has a mean pH level less than 6.5, which is the pH of the CVS brand water. Use a 5% significance level. Identify the following in your answer. 1. Identify the null Ho and alternative hypotheses H1 for the problem. 2. Identify the following: Sample statistic • Test Statistic (t): (Round to three decimal places) p - value: (Round to four places) • Calculator key used. 3. Identify the significance level and determine if you reject or fail to reject the null hypothesis. 4. State your conclusion.
There are two samples. Sample 1 has n=10 and a sample variance of 4. Sample 2 has n=8 and a sample variance of 9. Calculate the standard error of the difference between the two sample means (to 2 decimal points). Assume that the variances in the two populations that produced the samples are equal.
suppose that we have disjoint normal populations A and B and we want to find the standard error estimate for estimating the difference in their means. We have an IRS from A of size 8 with variance 25 and an IRS from B of size 9 with variance 16. What is the resulting standard error estimate if we assume both populations have the same population variance?
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The population mean will always be the same as the mean of all possible that can be computed from samples of size 27. True O False

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Suppose that X is a normal random variable with mean = 50.1 and standard deviation = 10.4. Let denote the variable for the process of taking a random sample and calculating the sample mean (We called this the