# Question: Let X equal the number of milliliters of a liquid

Let X equal the number of milliliters of a liquid in a bottle that has a label volume of 350 ml. Assume that the distribution of X is N(μ, 4). To test the null hypothesis H0: μ = 355 against the alternative hypothesis H1: μ < 355, let the critical region be defined by C = {x : x ≤ 354.05}, here x is the sample mean of the contents of a random sample of n = 12 bottles.

(a) Find the power function K(μ) for this test.

(b) What is the (approximate) significance level of the test?

(c) Find the values of K(354.05) and K(353.1), and sketch the graph of the power function.

(d) Use the following 12 observations to state your conclusion from this test:

(a) Find the power function K(μ) for this test.

(b) What is the (approximate) significance level of the test?

(c) Find the values of K(354.05) and K(353.1), and sketch the graph of the power function.

(d) Use the following 12 observations to state your conclusion from this test:

**View Solution:**## Answer to relevant Questions

Let X be N(μ,100). To test H0: μ = 80 against H1: μ > 80, let the critical region be defined by C = {(x1, x2, ... , x25) : x ≥ 83}, where x is the sample mean of a random sample of size n = 25 from this ...Let X1, X2, . . . , Xn be a random sample from the normal distribution N(μ, 9). To test the hypothesis H0: μ = 80 against H1: μ ≠ 80, consider the following three critical regions: C1 = {: ≥ C1}, C2 = {: ≤ C2}, ...A biologist is studying the life cycle of the avian schistosome that causes swimmer’s itch. His study uses Menganser ducks for the adult parasites and aquatic snails as intermediate hosts for the larval stages. The life ...Suppose that a third class (W) of 15 students was observed along with classes U and V of Exercise 9.2-3, resulting in scores of Again, use a chi-square test with α = 0.05 to test the equality of the three distributions by ...Different sizes of nails are packaged in “1-pound” boxes. Let Xi equal the weight of a box with nail size C, i = 1, 2, 3, 4, 5, where 4C, 8C, 12C, 16C, and 20C are the sizes of the sinkers from smallest to largest. ...Post your question