Solution Found!
A t-test is conducted for the null hypothesis H0: = 10
Chapter 7, Problem 116SE(choose chapter or problem)
A t-test is conducted for the null hypothesis \(H_0:\mu\ =\ 10\) versus the alternative \(H_a: \mu\ >\ 10\) for a random sample of n = 17 observations. The test results are t = 1.174, p-value = .1288.
a. Interpret the p-value.
b. What assumptions are necessary for the validity of this test?
c. Calculate and interpret the p-value assuming the alternative hypothesis was instead \(H_a: \mu\ \neq\ 10\).
Questions & Answers
QUESTION:
A t-test is conducted for the null hypothesis \(H_0:\mu\ =\ 10\) versus the alternative \(H_a: \mu\ >\ 10\) for a random sample of n = 17 observations. The test results are t = 1.174, p-value = .1288.
a. Interpret the p-value.
b. What assumptions are necessary for the validity of this test?
c. Calculate and interpret the p-value assuming the alternative hypothesis was instead \(H_a: \mu\ \neq\ 10\).
ANSWER:Solution :
Step 1 of 3:
Given a t-test is conducted for the null and alternative hypothesis are
againest
We know that the sample size n=17.
Then the t-test statistic is t=1.174 and the value of the p=0.1288.
Our goal is :
a). We need to interpret the p-value.
b). We need to find what assumption are necessary for the validity of this test.
c). We need to to calculate and interpret the p-value assuming the alternative hypothesis was instead .
a). Now we have to interpret the p-value.
We have to calculate p-value.
p=0.1288=P(t 1.174).
From the given information the value of p is not very small.
So there is no evidence to reject the null hypothesis for level of significance is less than or equal to 0.10.
Therefore, there is no evidence to indicate the mean is greater than 10.