Let Y, represent the ith normal population with unknown mean 4, and unknown varianceof for i=1,2. Consider independent random samples, Ya, Ya,the ith population with sample mean Y, and sample variance S? -Yin, of size n,, fromΤΗΣ (Υ) – Γ.) 2.(e) Is V₁ a pivotal function to find a confidence interval for o?? Explain with argument.(f) Find a (1-a) x 100% confidence interval for of(g) For non-zero constants a's, what is the distribution of U₂ = a₁Y₁-a₂Y₂? State allthe relevant parameters of the distribution.

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Answered: Let Y, represent the ith normal…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

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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Every year, the students at a school are given a musical aptitude test that rates them from 0 (no musical aptitude) to 5 (high musical aptitude). This year's results were: Aptitude Score 0 1 2 3 4 5 Frequency 4 1 1 4 4 1 The mean (T) aptitude score: The median aptitude score: (Please show your answer to 1 decimal place.) (Please separate your answers by ',' in bimodal situation. Enter DNE The mode aptitude score: if there is no mode.) Textbook Measures of Center
The sample mean and standard deviation from a random sample of 29 observations from a normal population were computed as ?¯=23x¯=23 and s = 6. Calculate the t statistic of the test required to determine whether there is enough evidence to infer that the population mean is greater than 21. Test Statistic =
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21 - The average weekly income of 50 students randomly selected from a class is 250 TL with a variance of 16, a weekly average working time of 15 hours and a variance of 16. The average weight of the students was 60 kg and the variance was 9, and the average of their height was 160 cm and the variance was 25. Based on this information, which of the following is true of the variable with the greatest variation between observations? a) Income variable B) Income and working time variable NS) Height variable D) Working time variable TO) Weight variable
An experiment is conducted to compare the maximum load capacity in tons (the maximum weight that can be tolerated without breaking) for two alloys A and B It is Kknown that the two standard deviations in load capacity are equal at 7 tons each. The experiment is conducted on 50 specimens of each alloy (A and B) and the results are X = 75.8. X = 71.8, and X-X=4. The manufacturers of alloy A are convinced that this evidence shows conclusively that Hug and strongly supports the claim that their alloy is superior. Manufacturers of alloy 8 claim that the experiment could easily have given X-X 4 even if the two population means are equal. Complete parts (a) and (b) below. Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table. (a) Make an argument that manufacturers of alloy B are wrong. Do it by computing P(XA-XB41 PA-HB) P(XA-X > 4) - @
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A random sample of n = 19 winter days in Denver gave a sample mean pollution index x1 = 43. Previous studies show that o1 = 10. For Englewood (a suburb of Denver), a random sample of n2 = 18 winter days gave a sample mean pollution index of x2 = 34. Previous studies show that o2 = 13. Assume the pollution index is normally distributed in both Englewood and Denver. Do these data indicate that the mean population pollution index of Englewood is different (either way) from that of Denver in the winter? Use a 1% level of significance. (a) What is the level of significance? State the null and alternate hypotheses. O Ho: H1 H2 O Ho: H1 = l2; H1: H1 < µ2 (b) What sampling distribution will you use? What assumptions are you making? O The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations. O The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations. O The Student's…
n,T 3. Suppose {uit}i=1,t=1 be i.i.d. variables with mean zero and variance o?. Show that for each i, Auit is autocorrelated. That is, Auit is correlated to some of its past values. E.g., it is enough to calculate Cov (Auit, Auit-1) and Cov (Auit, Auit-2) to see if any of these are non-zero.

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