R code:
p=1:5000*0
for(i in 1:5000)
{
x=rnorm(20,0,1)
t=abs(sqrt(20)*mean(x))
p[i]=2*(1-pnorm(t))
}
hist(p)
Q5: Uniform(0,1).
Q6. Yes.
Suppose X1, .., Xn is a random sample from a N(0, a2) population, where variance o...
9, A random sample is obtained from a population with variance = 400 and the sample mean is computed to be 70, Consider the null hypothesis Ho: μ = 80 versus the alternative H1: Ho: μ < 80. Compute the p-value. If n 32, the p-value is
A simple random sample of size n=40 is drawn from a population. The sample mean is found to be 106.9,and the sample standard deviation is found to be 15.1. Is the population mean greater than 100 at the α=0.025 level of significance? A) Determine the null and alternative hypotheses. B) Compute the test statistic C) Determine the P-value. (Round to three decimal places as needed.) D) What is the result of the hypothesis test? ____ the null hypothesis because the...
A random sample is obtained from a population with variance = 400 and the sample mean is computed to be 70. Consider the null hypothesis Ho: µ = 80 versus the alternative H1: Ho: µ < 80. Compute the p-value. If n = 16, the p-value is ?
Exercise 4.8: Suppose that X1, X2,..., Xn is a random sample of observations on a r.v. X, which takes values only in the range (0, 1). Under the null hypothesis Ho, the distribution of X is uniform on (0, 1), whereas under an alternative hypothesis, њ, the distribution is the truncated exponential with p.d.f. 0e8 where 6 is unknown. Show that there is a UMP test of Ho vs Hi and find, roximately, the critical region for such a test...
Let X1 Xn be a random sample of size n from a Bernoulli population with parameter p. Show that p= X is the UMVUE for p. 5.4.22 Let X1 Xn be a random sample of size n from a Bernoulli population with parameter p. Show that p= X is the UMVUE for p. 5.4.22
A random sample of n=25 is obtained from a population with variance σ^2, and the sample mean is computed. Test the null hypothesis H0 : μ = 110 versus the alternative hypothesis H1: μ>110 with α=0.01. Compute the critical value (Xc overbar) and state your decision rule for the options below. a. The population variance is σ^2=256. b. The population variance is σ^2=400. c. The population variance is σ^2=900. d. The population variance is σ^2=500.
Suppose a random sample of 100 observations from a binomial population gives a value of p = 0.45 and you wish to test the null hypothesis that the population parameter p is equal to 0.40 against the alternative hypothesis that p is greater than 0.40. Complete parts a through c. a. Noting that p = 0.45, what does your intuition tell you? Does the value of p appear to contradict the null hypothesis? O A. Yes, because p satisfies Hg:p>0.40...
6. Suppose that X1, ..., Xn is a random sample from a population with the probability density function f(x;0), 0 E N. In this case, the esti- mator ÔLSE = arg min (X; – 6)? n DES2 i=1 is called the least square estimator of Ô. Now, suppose that X1, ..., Xn is a random sample from N(u, 1), u E R. Prove that the least square estimator of u is the same as maximum likelihood estimator of u.
A random sample of 49 measurements from a population with population standard deviation o 3 had a sample mean of x, 9. An independeent random sample of sample mean of x, 11. Test the claim that the population means are 64 measurements from a second population with population standard deviation a2 4 had different. Use level of significance 0.01. (a) What distribution does the sample test statistic follow? Explain. The student's t. We assume that both population distributions are approximately...
2. Let X1,.n be a random sample from the density 0 otherwise Suppose n = 2m+ 1 for some integer m. Let Y be the sample median and Z = max(Xi) be the sample maximum (a) Apply the usual formula for the density of an order statistic to show the density of Y is (b) Note that a beta random variable X has density f(x) = TaT(可 with mean μ = α/(a + β) and variance σ2 = αβ/((a +s+...