7. The variance of a sample was reported to be 120. The report indicated that {(x-...
The variance of a sample was reported to be 144. The report indicated that = 7200. What has been the sample size? 49 50 51 52
OM 1. The standard deviation of a sample was reported to be 20. The report indicated that (x - 2)2 = 6800. What has been the sample size? A. 17 B. 18 C. 19 D. 21
7.109 Sample variance: Let X be a random variable with finite variance. Supposem don't know the variance of X and want to estimate it. You take a random sample, A1, sample, X1,..., X from the distribution of X and set S = (n − 1)-'L'=(X; - X)2. Show that the random variable 2-which is called the sample variance based on a sample of size n-is an unbiased estimator of oz.
7-27. Let X1, X2,..., X, be a random sample of size n from a population with mean u and variance o?. (a) Show that X² is a biased estimator for u?. (b) Find the amount of bias in this estimator. c) What happens to the bias as the sample size n increases?
6. Consider a sample X,... X, of normally distributed random variables with mean y and variance op. Let 5 be the sample variance and suppose that n = 16. What is the value of c for which p[x - SS (C2 - 1)] = 95 ? be the 7. Consider a sample X,...,X, of normally distributed random variables with variance o? = 30. Let S sample variance and suppose that n-61. What is the value of c for which P...
Find the variance of random variable X. 7.. Let X be a continuous random variable whose probability density function is: -(2x3 + ar', if x E (0:1) if x (0;1) Find 1) the coefficient a; 2) P(O.5eX<0.7); 3) P(X>3). Part 3. Statistics A sample of measurements is given X 8 -2 0 2 8
Suppose X, and X, are ramdom samples drawn from a population with mean ji and variance o?. Denote X = (1 - a)X1 +aX2. Find the value of a which minimize the variance of X. O1 O o 2 OO QUESTION 7 Let (X1, X2, ..., X16} be a random sample of size 16 from a normal pop- ulation having a mean of . The sample variance equals to 4. You want to test: HNS 4 versus H : >...
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and the variance of the sample mean X? e 800, 25 800, 2.5 o 0,1 o 0,2.5 QUESTION 5 Let Xi, X., In be a random sample from a population that is distributed accordingly to a discrete mass function (r). Denote E(X)= ?, the popu- lation mean.Consider an estimator for the population mean-??? ax. where ??-lai-1. What is E(0)? e+1 0 QUESTION Let Yi. Y... , be a raudom sample from a popnlation that is normally ted with ulíknowli...
2. Assume that the observed value of the sample mean X and of the sample variance S2 of a random sample of size n from a normal population is 81.2 and 26.5, respectively Find %90,%95, %99 confidence intervals for the population mean μ
2. Assume that the observed value of the sample mean X and of the sample variance S2 of a random sample of size n from a normal population is 81.2 and 26.5, respectively Find %90,%95, %99 confidence...
Using SPSS 2. A report indicated that the average family size was 3.18. A school district took a random sample of their families and came up with the data listed below. Is there a significant difference in this school district’s family size compared to the reported average? 5 6 5 4 3 2 5 3 4 2 4 7 3 4 6 5 4 2 3 2 3 2 5 3 a. State the null and alternate...