Let Y, represent the ith normal population with unknown mean , and unknown varianceof for i=1,2. Consider independent random samples, Ya, Y2.the ith population with sample mean Y, and sample variance S² =Yin, of size n,, from(Y-₁².(a) What is the distribution of Y,? State all the relevant parameters of the distribution.(b) Find a level a test (that is, the rejection region) for testing Ho : 4 = o versusHa i Pio when of is unknown and n, is small.:(e) In the context of the test in part (b), state the Type I error and give a probabilitystatement for the level of significance, a.

Given that the random variable represent the ith normal population with unknown mean and unknown…

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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Let x1, x2, . . . , x100 denote the actual net weights (in pounds) of 100 randomly selected bags of fertilizer. Suppose that the weight of a randomly selected bag has a distribution with mean 75 lbs and variance 1 lb2. Let x be the sample mean weight (n = 100). (a) Describe the sampling distribution of x. The distribution is approximately normal with a mean of 75 lbs and variance of 1 lb2.The distribution is approximately normal with a mean of 75 lbs and variance of 0.01 lbs2. The distribution is unknown with a mean of 75 lbs and variance of 0.01 lbs2.The distribution is unknown with a mean of 75 lbs and variance of 1 lb2.The distribution is unknown with unknown mean and variance. (b) What is the probability that the sample mean is between 74.65 lbs and 75.35 lbs? (Round your answer to four decimal places.) P(74.65 ≤ x ≤ 75.35) = (c) What is the probability that the sample mean is greater than 75 lbs?
Let wages denote hourly wages, educ years of education, and exper years of experience, and suppose log(wages) = f1 + 62educ + B3exper +e where E[eleduc, exper] = 0. Let b1, b2, and bz be our estimates for B1, B2, and ß3 and r23 denote the sample correlation between {educ,}", and {exper, }". Which of the following statements is true? II O a. The variance of b3 does not depend on r23. O b. The variance of b, is increasing in E" (educ, – educ,)² (all else equal). O c. The variance of b2 is at least as large as o²/ E", (educ, - educ,)2 for o? Var(eleduc, exper). O d. The variance of b2 depends on the sign of r23. O e. The variance of b2 always increases as r23 increases (all else equal).
1. One difference between ANOVA and regression is: a) ANOVA is for statistical inference, whereas regression is not b) a regression line accounts for variability, whereas variability is not a concept in ANOVA c) in regression, we estimate a slope, whereas in ANOVA, we estimate mean differences d) ANOVA bases its inferences on samples, whereas regression bases its inferences on populations e) ANOVA and regression are not different at all, they are exactly the same f) ANOVA features p-values, whereas regression does not
9. (8') Let X,, X,, X, be a sample of size n=3 from a distribution with unknown mean u, -0 < u<0, where the variance o is a known positive number. Show that both à =i and ê, = 2X, + X, +5X, are unbiased estimators for H.
A standardized exam’s score are normally distributed. In a recent year, the mean test score was 1477 and the standard was 315. The test scores of four students selected at random 1860 1230, 2160, and 1360. Find the Z- score that correspond to each value and determine wether any of the values are unusual. The Z-score for 1860 is-The Z-score for 1230 is-The Z-score for 2160 is-The Z-score for 1360is-
Say you have two sets of data X1, ..., X10 and Y1,..., Y40. All of this data is considered independent. The first set of data are Normally distributed with mean B and variance 10. The second set of data are Normally distributed with mean y and variance 10. We are trying to estimate 0 = X = X; 18 + y. Consider the estimate ô = }X + Ÿ where 3 4 iX + Y where 10 vi=1 1 10 and Y = E Y;? 40 vi=1 40 (a) What is the mean, variance and distribution of 0? (b) What is the probability that 0 is larger than 1 away from 0? (c) What is the bias, variance and MSE of the estimate 0 for estimating 0?
A distribution with u=55 and o=6 is being standardized so that the new mean and standard deviation will be u =50 and o=10.When the distribution is standardized,which value will be obtained for a score of x=58 from the original distribution? x=53 x=55 X=58 x=61
12. Let (*1, 12, ., r„) be independent samples from the uniform distribution on [0,0]. Let X(n) and X(1) be the maximum and minimum order statistics respectively, (a) Find the distribution of X(m) and X(a) and hence, their means and variances. X{n) (b) Show that 2nY x where Y = – In %3D (c) Show that 2) In - Xản: Hence write a function of the geometric mean, i=1 (II GM(r) = which is Xn 1
Vehicle speeds at a certain highway location are believed to have approximately a normal distribution with mean µ = 50 mph and standard deviation σ = 5 mph. The speeds for a randomly selected sample of n = 25 vehicles will be recorded. (a) Give numerical values for the mean and standard deviation of the sampling distribution of possible sample means for randomly selected samples of n = 25 from the population of vehicle speeds. Mean = s.d.(x) = (b) Use the Empirical Rule to find values that fill in the blanks in the following sentence. For a random sample of n = 25 vehicles, there is about a 95% chance that the mean vehicle speed in the sample will be between and mph. (c) Sample speeds for a random sample of 25 vehicles are measured at this location, and the sample mean is 59 mph. Given the answer to part (b), explain whether this result is consistent with the belief that the mean speed at this location is μ = 50 mph. A sample mean of 59 mph (when n = 25) --Select--- be consistent with…
Course: StatisticsA study conducted on the number of vehicles arriving per hour at a toll booth established the following results: The mean number of vehicles arriving per hour is 39, the standard deviation is 6 vehicles per hour, the proportion of trucks with respect to the total number of vehicles passing through the toll booth is 12%, according to these data, which one or ones are necessary to establish a Poisson distribution to measure the estimated number "X" of vehicles per hour?I. The average of 39 vehicles per hour.II. The standard deviation of 6 vehicles per hour.III. The ratio of 12% trucks. Select one:a. Only Ib. Only II.c. Only III.d. I and II.e. I and III.

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