Let X11 X12X1, and X2₂1, X22, X2na be two independent random samples ofsize ni and n₂ from two normal populations N(₁, of) and N(2, 2) respectively.(d) Derive a (1-a) x 100% confidence interval for (₁-2) when both samples aresmall but of and o are known.(e) Discuss how the confidence interval in part (c) will change if both the samples arelarge.

Given that samples are random and independent. The size of the samples is small and the population…

Answered: Let X₁1X12X1, and X21, X22X2, be two…

A First Course in Probability (10th Edition)

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Chapter1: Combinatorial Analysis

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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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(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
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2. We performed a linear regression using 25 observations. From the regression output we find that bo = 5.7, bị = 12.9, x = 11.4, Sz = 3.2 and MSE = 12.25. a. From the least squares line, what is the predicted response when x* = 10.65? y = b. What is the 95% confidence interval for the mean response when x* = 10.65? c. What is the 95% prediction interval for an individual response when x* = 10.65? d. Which interval is wider? The confidence interval or the prediction interval? O a. Confidence Interval b. Prediction Interval
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Let X₁1X12X1, and X21, X22X2, be two independent random samples of size ny and n₂ from two normal populations N(₁, of) and N(2, 2) respectively. (d) Derive a (1-a) x 100% confidence interval for (μ₁ −µ₂) when both samples are small but of and of are known.