(In some of the exercises that follow, we must

Chapter 9, Problem 9E

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QUESTION:

Let \(X_i, i = 1, 2, 3, 4\), equal the distance (in yards) that a golf ball travels when hit from a tee, where i denotes the index of the ith manufacturer. Assume that the distribution of \(X_i\) is \(N(\mu_i, \sigma^2), i = 1, 2, 3, 4\), when a ball is hit by a certain golfer. We shall test the null hypothesis \(H_0: \mu_1 = \mu_2 = \mu_3 = \mu_4\), using three observations of each random variable.

(a) Give a critical region for an \(\alpha = 0.05\) significance level.

(b) Construct an ANOVA table and state your conclusion, using the following data:

               \(x_1: 240 \quad 221 \quad 265\)

               \(x_2: 286 \quad 256 \quad 272\)

               \(x_3: 259 \quad 245 \quad 232\)

               \(x_4: 239 \quad 215 \quad 223\)

(c) What would your conclusion be if \(\alpha = 0.025\)?

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

Questions & Answers

QUESTION:

Let \(X_i, i = 1, 2, 3, 4\), equal the distance (in yards) that a golf ball travels when hit from a tee, where i denotes the index of the ith manufacturer. Assume that the distribution of \(X_i\) is \(N(\mu_i, \sigma^2), i = 1, 2, 3, 4\), when a ball is hit by a certain golfer. We shall test the null hypothesis \(H_0: \mu_1 = \mu_2 = \mu_3 = \mu_4\), using three observations of each random variable.

(a) Give a critical region for an \(\alpha = 0.05\) significance level.

(b) Construct an ANOVA table and state your conclusion, using the following data:

               \(x_1: 240 \quad 221 \quad 265\)

               \(x_2: 286 \quad 256 \quad 272\)

               \(x_3: 259 \quad 245 \quad 232\)

               \(x_4: 239 \quad 215 \quad 223\)

(c) What would your conclusion be if \(\alpha = 0.025\)?

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

ANSWER:

Step 1 of 5

Given:

The distance that a golf ball travels when hit from a tee is. It follows normal distribution written as: .  

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