The following information is available.
H0: mean of population<= 10
H1: mean of population > 10
The sample mean is 12 for a sample of 36. The population standard
deviation is 3. Use the .02 significance level
(a) Is this a one- or two-tailed test?
One-tailed
(b) What is the decision rule?
Reject the null hypothesis if the test statistic falls in the critical region.
Otherwise, don’t reject.
The critical region is z> 2.05, this comes from looking up alpha = 0.02 in the
z-table to find the z-value which cuts off the upper 0.02 region of the
sampling distribution.
So the more specific decision rule is:
Reject the null hypothesis if the test statistic is greater than 2.02.
Otherwise, don’t reject.
(c) What is the value of the test statistic?
Z = (12-10)/(3/sqrt36) = 2/(3/6) = 2/(1/2) = 4
(d) What is your decision regarding H0?
4 > 2.02. the test statistic DOES fall in the critcal region. So, we reject the
null hypothesis
(e) What is the p-value? Interpret it.
P = 0.00003
The test statistic of 4 cuts off the 0.00003 region of the sampling
distribution.
That is 0.003 % of the sampling distribution falls above a z-value of 4