Question 0. Let X₁,, Xn be iid random variables with unknown mean u and unknown variance0². Let Xn=1 Xi and S² = n11(Xi - Xn)² be the sample based estimators of u ando2, respectively. Show S2 is an unbiased estimator of o2 (see the lecture notCIMIDC

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Answered: Question 0. Let X₁, , Xn be iid 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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We are running a hypothesis test to see if weight of African zebras is significantly different than that of Arabian horses. We assume weight in both populations is normally distributed and both populations have the same population variance in weight which is unknown to us, so we use the sample variances to estimate the standard error for our calculations. We have a sample of size 9 for the African zebras with mean 650 and a sample of size 16 for the Arabian horses with mean 660. If the pooled variance is 225, then what is the absolute value of the standardized test statistic for our data?
The nation of Olecarl, located in the South Pacific, has asked you to analyze international trade patterns. You first discover that each year it exports 10 units and im- ports 10 units of wonderful stuff. The price of exports is a random variable with a mean of 100 and a vari- ance of 100. The price of imports is a random variable with a mean of 90 and a variance of 400. In addition, you discover that the prices of imports and exports have a correlation of r = -0.40. The prices of both ex- ports and imports follow a normal probability density function. Define the balance of trade as the difference between the total revenue from exports and the total cost of imports. What are the mean and variance of the balance of trade? What is the probability that the balance oft trade is negative?
We are running a hypothesis test to see if blood pressure of African zebras differs significantly from Arabian horses. We assume blood pressure in both populations is normally distributed and both populations have the same population variance in blood pressure which is unknown to us, so we use the sample variances to estimate the standard error for our calculations. We have a sample of size 9 for the African zebras and a sample of size 16 for the Arabian horses. How many degrees of freedom does our test statistic have?
1. Exploring the role of level of confidence: b. Construct 1,000 confidence intervals with n = 100, p = 0.3. What proportion of the99% confidence intervals included the population proportion, 0.3? Reset and Construct another 1,000 confidence intervals with n = 100, p = 0.3. Whatproportion of the 99% confidence intervals included the population proportion, 0.3? Did the same proportion of intervals include the population proportion each time?What proportion did you expect to include the population proportion in each part?
Suppose we flip three fair coins. Let X = number of Heads.(a) Calculate the variance of X directly by using ONLY the PMF for X and theformula for variance (b) Calculate the variance again, but this time, use some of the tools from thebottom of page 9 (split X into 3 Bernoulli r.v.s).(c) Let Y = three times the Bernoulli r.v. for the first coin. Calculate Var(Y ).(d) Explain why your answer to Part C is different from Parts A and B.
How do I get the variance ?
When a random variable X follows binomial distribution, the probability of success on one trian is equal to 0.6, and the number of trials is eual to 120, What is the variance of X ? |------
8 If the analysis of variance F-test leads to the conclusion that at least one of the model parameters is nonzero, can you conclude that the model is the best predictor for the dependent variable y? Can you conclude that all of the terms in the model are important for predicting y? What is the appropriate conclusion?
A researcher is interested whether a new drug is effective in changing patients' cholesterol levels. She divided 33 patients into 3 groups according to the dosage the patient received. The cholesterol levels of all patients are measured and used as the data for the Analysis of Variance (ANOVA). If she reported the test statistic F = 2.1 What is the degree of freedom for the numerator of the F statistic? What is the degree of freedom for the denominator of the F statistic? What is the P-value of the F-test? (Round to 3 decimals) Given the significance level of 0.01, what can she conclude from the test? *The patients in differnt groups have simliar average cholesterial levels. The drug made no difference. *At least one group of patients have an average cholesterol level that is different from the other groups. The drug may have an effect.
We are running a hypothesis test to see if weight of African zebras is significantly different than that of Arabian horses. We assume weight in both populations is normally distributed and both populations have the same population variance in weight which is unknown to us, so we use the sample variances to estimate the standard error for our calculations. We have a sample of size 9 for the African zebras with mean 650 and a sample of size 16 for the Arabian horses with mean 659. If the pooled variance is 81, then what is the absolute value of the standardized test statistic for our data?
Two separate samples, each with n = 14 individuals, receive different treatments. After treatment, the first sample has SS = 1512 and the second has SS = 1620. Find the pooled Variance for two independent samples. (hundredths place) Type only the pooled variance.
The data shown in the table represent the measurements of 10-kΩ resistors (in kΩ) produced from five different machines. A random sample of nine resistors from each machine is taken to determine whether the mean resistance varies from one machine to another. Perform analysis of variance and test the hypothesis at the 0.05 level of significance that the mean resistances differ significantly for the five machines, all through manual computations. Show all complete and systematic solutions.

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Question 0. Let X₁, , Xn be iid random variables with unknown mean u and unknown variance - 0². Let Xn=1 Xi and S² = 11 (Xi - Xn)² be the sample based estimators of u and o2, respectively. Show S2 is an unbiased estimator of o2 (see the lecture not