= 20 versus H,: <20. A sample of size n=52 is drawn, and x = 18. The population standard deviation A test is made of H: is o=6 (a) Compute the value of the test statistic Z. (b) is Ho rejected at the a=0.05 level? (c) Is H, rejected at the a=0.01 level?
4.18 A random sample of size 25 is selected from a population with mean μ = 85 and standard deviation σ-4. Approximate the following probabilities using the central limit theorem (a) PrX 86, 6451 (b) PrX < 84.340] (c) Pr(83.04 〈 X < 86.96]
Let X, X,, ..., X, denote a random sample of size n from a population with pdf (10) = b exp(@m()).0<x<1 where (<O<0. Derive that the likelihood ratio test of H.:0=1 versus H, :0 #1 in terms of T(x) = ŽI (3)
Problem 3 Let X1, X2, ... , Xn be a random sample of size n from a Gamma distribution fr; a,B) 22-12-1/B, 0 < < (a) Find a sufficient statistics for a. (b) Find a sufficient statistics for B.
A) B) C) 1 Find the Laurent series for 22 +22 for 0 < 121 < 2 Find the Laurent series for (z+2)}(3-2) for 2 – 3) > 5 1 Find the Laurent series for z2(z-i) for 1 < 12 – 11 < V2
Problem 5 Let Y1 denote the minimum of a random sample of size n from a distribution that has pdf f(x) e(,0x< o0, zero elsewhere X- n (Y1 0), find the cumulative distribution function (cdf) for Zn = n (Y1 - 0), and Let Zn find the limiting cdf of Zn as n >oo.
1. Consider a random sample of size n from a population with pdf: f (x) = (1 -p-p, 0 <p<1, x= 1, 2, ... (a) Show that converges in probability to p. (b) Show that converges in probability to p (1 – p). (c) Find the limiting distribution of
Suppose you are given a population of size 500 with a mean of 85 and a standard deviation of 14. If you take a simple random sample of size 40, what is the probability that the sample mean will be smaller than 87? (to 4 decimals) Plă < ) = P(Z < (Hint: Don't forget to check the value of n/N.)
Question Help To test Ho: -50 versus H: <50, a random sample of size n=25 is obtained from a population that is known to be normally distributed. Complete parts (a) through (d) below. Click here to view the t-Distribution Area in Right Tai (a) If x= 46.6 and s-13.8, compute the test statistic. to=(Round to three decimal places as needed.) (b) If the researcher decides to test this hypothesis at the c 0.05 level of significance, determine the critical value(s)....
Let X N(1,3) and Y~ N(2,4), where X and Y are independent 1. P(X <4)-? P(Y < 1) =? 4、 5, P(Y < 6) =? 7, P(X + Y < 4) =?