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 \(i\) th manufacturer. Assume that the distribution of \(X_{i}\) is \(N\left(\mu_{i}, \sigma^{2}\right), i=1,2,3,4\), 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:

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

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

Equation Transcription:

:

Text Transcription:

X_i, i=1,2,3,4

i

X_i

N(mu_i, sigma^2),i=1,2,3,4

H_0: mu_1=mu_2=mu_3=mu_4

alpha=0.05

alpha=0.025

p

Step 1 of 5

Given:

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