Solution Found!
(In some of the exercises that follow, we must
Chapter 9, Problem 9E(choose chapter or problem)
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: .