a) Suppose we know the population variance σ2-400, there is a randorm sample with i-135, and...
Suppose you wish to estimate the mean of a normal population using a 95% confidence interval, and you know from prior information that σ2 ≈ 1. a. To see the effect of the sample size on the width of the confidence interval, calculate the width of the confidence interval for n = 16, 25, 49, 100, and 400. b. Plot the width as a function of sample size n on graph paper. Connect the points by a smooth curve and...
6. Consider the following sample: Xi = -2, X2 = 12. X7-1.5, Xs -0.5, a. Estimate the population mean, μ, using an analogical estimator. b. Estimate the population variance. ơ2, using a biased and an unbiased estimator. c. Assuming that the random sample is drawn from a normal population with known variance, σ2-4, construct a 95% confidence interval for the population mean. d. Assuming that the random sample is drawn from a normal population with unknown variance, σ2, construct a...
1. Suppose you are drawing a random sample of size n > 0 from N(μ, σ2) where σ > 0 is known. Decide if the following statements are true or false and explain your reasoning. Assume our 95% confidence procedure is (X- 1.96X+1.96 Vn a. If (3.2, 5.1) is a 95% CI from a particular random sample, then there is a 95% chance that μ is in this interval. b. If (3.2.5.1) is a 95% CI from a particular random...
We draw a random sample of size 25 from a normal population with a known variance of 2.4. If the sample mean is 12.5, what is the Lower Confidence Limit for the 95% confidence interval for the population mean? Include 1 decimal place in your answer
Let X = (X1, . . . , Xn) be a random sample of size n with mean μ and variance σ2. Consider Tm i=1 (a) Find the bias of μη(X) for μ. Also find the bias of S2 and ỡXX) for σ2. (b) Show that Hm(X) is consistent. (c) Suppose EIXI < oo. Show that S2 and ỡXX) are consistent.
Let X = (X1, . . . , Xn) be a random sample of size n with mean μ...
Suppose that X1, X2n is a random sample of size 2n from a population with mean μ and variance σ2 for which the first four moments are finite. Find the limiting distribution to which the following random sequence converges in probability: 7l
Suppose that X1, X2n is a random sample of size 2n from a population with mean μ and variance σ2 for which the first four moments are finite. Find the limiting distribution to which the following random sequence...
I. Suppose population 1 has mean μ1 with variance σ2 and population 2 has mean μ2 denote the sample variances from two samples with the same variance σ2 Let s and s with size n and n2 from the corresponding populations, respectively. Show that the pooled estimator pooled n1 2 - 2 is an unbiased estimator of σ2
1. A random sample of 25 observations was selected from a normally distributed population. The average in the sample was 84.6 with a variance of 400.a. Construct a 90% confidence interval for μ.b. Construct a 99% confidence interval for μ.c. Discuss why the 90% and 99% confidence intervals are different.d. What would you expect to happen to the confidence interval in part (a) if the sample size was increased? Be sure to explain your answer.
Suppose you take a random sample of 30 individuals from a large population. For this sample, the sample mean is 4.2 and sample variance is 49. You wish to estimate the unknown population mean µ. (a) Calculate a 90% confidence interval for µ. (b) Calculate a 95% confidence interval for µ. (c) Based on (a) and (b), comment on what happens to the width of a confidence interval (increase/decrease) when you increase your confidence level. (d) Suppose your sample size...
A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, x overbar, is found to be 108, and the sample standard deviation, s, is found to be 10. (a) Construct a 95% confidence interval about mu if the sample size, n, is 25. (b) Construct a 95% confidence interval about mu if the sample size, n, is 12. (c) Construct a 70% confidence interval about mu if the sample size, n,...