Given the following hypothesis H0 400 H1 400 A random sampl

Given the following hypothesis: H0: = 400 H1: 400 A random sample of 12 observations is selected from a normal population. The sample mean was 407 and the sample standard deviation 6. Using the .01 significance level:

a) State the decision rule.

b) Compute the value of the test statistic.

c) What is your decision regarding the null hypothesis?

Solution

Given n=12, xbar=407, s=6

a. Given a=0.01, the critical values are |t(0.005, df=n-1=11)|=3.11 or -3.11 (check student t table)
If t<-3.11 or t>3.1, we reject Ho.


b. The test statistic is
t=(xbar-u)/(s/n)

=(407-400)/(6/sqrt(12))

=4.04

c. Since t=4.04 is larger than 3.1, we reject Ho.