TOPIC: Distribution of sample variance for a Normal population.
I. Consider a random sample of size n from a normal population with variance σ (n-1s2...
Suppose that X, and X, are means of two random samples of size n from a population with variance σ. Determine n such that the probability will be about 0.01 that the two sample means will differ by more than ơ . [Hint: Consider 4.
Suppose that X, and X, are means of two random samples of size n from a population with variance σ. Determine n such that the probability will be about 0.01 that the two sample means...
Consider a random sample of size n from an infinite population
with mean μ and variance σ2.
6. Consider a random sample of size n from an infinite population with mean μ and variance σ2. (a) Find the method of moments estimator for μ in terms of the sample moments (b) Find the method of moments estimator for σ2 in terms of the sample moments.
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...
Consider a random sample from a normal population with mean u = 3 and variance o2 = 22, with sample size n = 20. Suppose the sample variance is 82 = 2.72. Let p be the probability that s2 exceeds the sample variance 52. Which of the following is true? 0.01 < p < 0.025 0.025 < p < 0.05 0.05<P 0.005< p < 0.01 Op < 0.005
Consider a random sample from a normal population with mean u = 3 and variance o2 = 22, with sample size n = 20. Suppose the sample variance is 82 = 2.72. Let p be the probability that s2 exceeds the sample variance 52. Which of the following is true? 0.01 < p < 0.025 0.025 < p < 0.05 0.05<P 0.005< p < 0.01 Op < 0.005
Consider a random sample from a normal population with mean u = 3 and variance o2 = 22, with sample size n = 20. Suppose the sample variance is 82 = 2.72. Let p be the probability that s2 exceeds the sample variance 52. Which of the following is true? 0.01 < p < 0.025 0.025 < p < 0.05 0.05<P 0.005< p < 0.01 Op < 0.005
. A random sample of size n is taken from a population that has a distri- bution with density function given by 0, elsewhere Find the likelihood function L(n v.. V ) -Using the factorization criterion, find a sufficient statistic for θ. Give your functions g(u, 0) and h(i, v2.. . n) - Use the fact that the mean of a random variable with distribution function above is to find the method of moment's estimator for θ. Explain how you...
5. Do you agree with the first three statements below? If yes, justify briefly. If not, correct it. For the last part, describe in a paragraph. If X is the mean of a random sample of size n froma population with the mean μ and the variance σ2, then its sampling distribution is a normal with the mean μ and the variance σ-, Agree Disagree If S2 is the variance of a random sample of size n taken from any...
A population of values has a normal distribution with μ=89.8 and σ=85.9. You intend to draw a random sample of size n=131. What is the mean of the distribution of sample means? μx¯= What is the standard deviation of the distribution of sample means (i.e. the standard error)? (Report answer accurate to 2 decimal places.) σ¯x=
Suppose
that Y1 , Y2 ,..., Yn denote a random sample of size n from a
normal population with mean μ and variance 2 .
Problem # 2: Suppose that Y , Y,,...,Y, denote a random sample of size n from a normal population with mean u and variance o . Then it can be shown that (n-1)S2 p_has a chi-square distribution with (n-1) degrees of freedom. o2 a. Show that S2 is an unbiased estimator of o. b....