Solution Found!
Refer to Exercise 7.84. Suppose we had n = 100, = 9.4, and
Chapter 7, Problem 85E(choose chapter or problem)
Refer to Exercise 7.84. Suppose we had n = 100, \(\bar{x}=9.4\), and \(s^2=4.84\)..
a. Test the null hypothesis, \(H_0:\sigma^2\ >\ 1\), against the alternative hypothesis, \(H_0:\sigma^2\ >\ 1\).
b. Compare your test result with that of Exercise 7.84.
Questions & Answers
QUESTION:
Refer to Exercise 7.84. Suppose we had n = 100, \(\bar{x}=9.4\), and \(s^2=4.84\)..
a. Test the null hypothesis, \(H_0:\sigma^2\ >\ 1\), against the alternative hypothesis, \(H_0:\sigma^2\ >\ 1\).
b. Compare your test result with that of Exercise 7.84.
ANSWER:Solution:
Step 1 of 2:
From exercise 7.84. We have n = 100, and
a). To test the null hypothesis against
.
Given the hypotheses are
against
The test statistic is
= 479.16
The rejection region requires in the upper tail of the
distribution with
df = n -1 = 100 - 1 = 99.
(this value from the critical value of the chi-square distribution)
The rejection region is
Here we conclude that, the test statistic is greater than the table value.
That is, . So
is rejected.
Therefore, there is sufficient evidence to indicate the variance is larger than 1 at