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:
.