3. The example from lectures (the liquid filling machine) is considered for the second time. We will again assume that the machine fills the canisters with liquid and volume of liquid (in liters) within each canister follows approximately the normal distribution N(μ, 2) and the amount of liquid in each canister is thought to be independent one another. This time, 16 measurement results have been collected and (again) we assume μ and σ² > 0 are unknown. Suppose now that the measurements (in liters) are as below y = (9.88, 10.11, 10.33, 10.47, 9.84, 10.17, 10.13, 10.58, 10.22, 10.72, 10.07, 10.33, 10.04, 10.45, 10.16, 9.47) Using the data determine (a) some one-sided 99% confidence interval for parameter μ. (b) two-sided symmetric 99% confidence interval for parameter μ.

1. The sample mean weights for two varieties of lettuce grown for 16 days in a controlled environment are 3.259 and 1.413 and the corresponding sample standard deviations are .400 and .220. If the sample sizes for the two varieties are 9 and 6 respectively, what would be the pair of hypotheses to test if the two varieties of lettuce have the same average weight? (Given: weight of each variety of lettuce is normally distributed).   A. H0: μ1 ≠ μ2 vs H1: μ1 = μ2 B. H0: μ1 = μ2 vs H1: μ1 ≠ μ2 C.H0: μ1 > μ2 vs H1: μ1 ≤ μ2 D. H0: μ1 ≤ μ2 vs H1: μ1 > μ2   2. What is the best decision using critical value approach in problem 1? A. The computed test statistic falls in the critical region and we do not reject the null hypothesis.   B. The computed test statistic does not fall in the critical region and we do not reject the null hypothesis.   C. The computed test statistic falls in the critical region and we reject the null hypothesis.   D. The computed test statistic does not fall…

A doctor wants to research if there is any difference in the birth weights of a mother's first child and second child. Suppose that data were collected for a random sample of 10 mothers with 2 children, where each difference is calculated by subtracting the weight of the first child from the weight of the second child. Assume that the weights are normally distributed. The doctor uses the alternative hypothesis Ha:μd≠0. Suppose the test statistic t is calculated as −1.101, which has 9 degrees of freedom. If the p-value is greater than 0.10 and the significance level is α=0.10, what conclusion can be made about the birth weights of a mother's first 2 children? Select all that apply:   Reject the null hypothesis.     Fail to reject the null hypothesis.     The conclusion of the hypothesis test is that there is sufficient evidence to suggest that the birth weights of a mother's first 2 children are different.     The conclusion of the hypothesis test is that…

Suppose X, Y, Z are iid observations from a Poisson distribution with parameter λ, which is unknown. Consider the 3 estimators T1 = X + Y − Z, T2 = 2X + Y + Z 4 , T3 = 3X + Y + Z 5 . (a) Which among the above estimators are unbiased? (b) Among the class of unbiased estimators, which has the minimum variance?

Suppose the random variables X and Y are inde lent and identically distributed. Let Z =aX +Y. If the correlation coefficient between X and Z is1/3 , then what is the value of the constant a ?

In case of omitted variable bias, which of the following OLS assumption will be violated Group of answer choices (X,Y) are i.i.d. drawn from their joint distribution E(u|X)=0 There are no outliers for X and u. There is heteroskedasticity.