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Please answer Problems 1-5 (with all the parts) and please show the work/steps! Thank you!

1/2 STA103_HW6.pdf Due Friday Dec 7th Problem 1. (problem 10.3 page 194) We have a simple random sample of size 4 from a population with mean u. Consider the following two estimators of u 10 10 a. Show that both μ1 and μ2 are unbiased estimators for μ. b. Which one is better? Fully justify your answer Problem 2. (Problem 10.4 page 194) Suppose that we have independent samples of size 10 and 15, respectively, from a population with mean μ. We calculate the sample mean for each sample and refer to them as X1o and Xi5 a. Is Xio or X15 a better estimator of ? Fully justify your answer b. Consider the following ways of combining X10 and X15 to form a single est innate of μ: 15. 15 10 25 The difference has to do with whether the sample means are equally weighted or given differential weights based upon the different sample sizes. Which estimator is better? Fully justify your answerSTA103_HW6.pdf weights based upon the different sample sizes. Which estimator is better Fully justify your answer Problem 3. (problem 10.13 page 200) Consider the following two estimators of the population mean μ based on a random sample of size 4 from a population with mean μ and variance σ2 Calculate the mean squared error of each estinator. For what values of μ and σ2 the muse(A) < mse(i2)? Problem 4. (problem 11.7 page 220) As a financial aid officer at a large university, you are interested in the mean summer income of students. To investigate this, you take a simple random sample of 100 students and find -$2000 with S-$500. Build a 95% Confidence interval for the mean summer income of all students withi Problem 5. (problem 11.8 page 220) A simple random sample of 25 recent graduates from ia particular college gives a sample mean starting salary of $24,000 with sample standard deviation $3000. Build a 95% confidence interval for the mean starting salary of all graduate students form this college n this population

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