# Question

Let X and Y equal the forces required to pull stud No. 3 and stud No. 4 out of a window that has been manufactured for an automobile. Assume that the distributions of X and Y are N(μX, σ2x) and N(μY, σ2Y), respectively.

(a) If m = n = 10 observations are selected randomly, define a test statistic and a critical region for testing H0: μX − μY = 0 against a two-sided alternative hypothesis. Let α = 0.05. Assume that the variances are equal.

(b) Given n = 10 observations of X, namely,

and m = 10 observations of Y, namely,

Calculate the value of the test statistic and state your conclusion clearly.

(c) What is the approximate p-value of this test?

(d) Construct box plots on the same figure for these two sets of data. Do the box plots confirm your decision in part (b)?

(a) If m = n = 10 observations are selected randomly, define a test statistic and a critical region for testing H0: μX − μY = 0 against a two-sided alternative hypothesis. Let α = 0.05. Assume that the variances are equal.

(b) Given n = 10 observations of X, namely,

and m = 10 observations of Y, namely,

Calculate the value of the test statistic and state your conclusion clearly.

(c) What is the approximate p-value of this test?

(d) Construct box plots on the same figure for these two sets of data. Do the box plots confirm your decision in part (b)?

## Answer to relevant Questions

Let X and Y denote the tarsus lengths of male and female grackles, respectively. Assume that X is N(μX, σ2x) and Y is N(μY, σ2Y). Given that n = 25, x = 33.80, s2 x = 4.88, m = 29, y = 31.66, and s2y = 5.81, test the ...A bowl contains two red balls, two white balls, and a fifth ball that is either red or white. Let p denote the probability of drawing a red ball from the bowl. We shall test the simple null hypothesis H0: p = 3/5 against the ...Data were collected during a step-direction experiment in the biomechanics laboratory at Hope College. The goal of the study is to establish differences in stepping responses between healthy young and healthy older adults. ...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: ...Assume that the weight X in ounces of a “10- ounce” box of cornflakes is N(μ, 0.03). Let X1, X2, . . . , Xn be a random sample from this distribution. (a) To test the hypothesis H0: μ ≥ 10.35 against the alternative ...Post your question

0