# Question: Let X and Y equal the forces required to pull

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)?

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