b) Let X1, X2, .,X, be a random sample from a normal distribution with known....mean u. Using a distribution of U = E, , Mr Mbalula showed that a100(1 – a)% two sided confidence interval for o? is give byE(X – 4)² £=(X; – µ) |xả.Prove whether or not Mr Mbalula is correct.

Answered: Image /qna-images/answer/bdff0264-72b7-4e51-9b18-d9e5fd094a8b.jpg

Answered: b) Let X1, X2, .,X, be a random sample…

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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The calibration of a scale is to be checked by weighing a 10-kg test specimen 25 times. Suppose that the results of different weighings are independent of one another and that the weight on each trial is normally distributed with = 0.2 kg. Let μ denote the true average weight reading on the scale. (a) What hypotheses should be tested? (b) What is the p-value when = 9.85? What would you conclude at significance level a = 0.01?
1) Your instructor tells you that past average scores for the final exam are 75%. But this semester he has been using online quizzes to help your class better prepare for the final. Your class scored the following on the final exam: mean= 80% with a 10% standard deviation. There are 49 people in your class. Using a one-sample t test, what is your t score for this class? Assuming α = .05, did the online quizzes help your class perform better?
Suppose that one chemical plant in a large corporation is accused of exceeding the established limits of toxins being released into the atmosphere. A decision is made to test whether or not the mean level of toxins exceeds the tolerance level μ0=100μ0=100 ppm (parts per million). How would the null and alternative hypotheses be set up given that the researcher is working for the corporation? How would those hypotheses change if the researcher is working for the Environmental Protection Agency (EPA)?
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To evaluate the effect of a treatment, a sample is obtained from a population with a mean of 20 and the treatment is administered to the individuals in the sample. After treatment, the sample mean is found to be X = 17.7 with a standard deviation of ô = 3. (a) If the sample consists of N = 16 individuals, are the data sufficient to conclude that the treatment decreases scores? (b) If the sample consists of N = 36 individuals, are the data sufficient to conclude that the treatment decreases scores? (c) Comparing your answers for parts (a) and (b), how does the size of the sample influence the size of the obtained Bayes factor?
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b) Let X1, X2, .,X, be a random sample from a normal distribution with known mean u. Using a distribution of U = E-1 Mr Mbalula showed that a 100(1 – a)% two sided confidence interval for o? is give by E(X; - 4)? E%(X; – µ)² Prove whether or not Mr Mbalula is correct.