In: Statistics and Probability
Consider the following hypotheses:
H0: μ ≤ 12.6
HA: μ > 12.6
A sample of 25 observations yields a sample mean of 13.4. Assume that the sample is drawn from a normal population with a population standard deviation of 3.2.
a. Calculate the value of the test statistic.
b. Find the p-value.
c. Calculate the critical value using α = 0.05
d. What is the conclusion if α = 0.05? Interpret the results at α = 0.05.
e. Calculate the p-value if the above sample mean was based on a sample of 100 observations.
f. Based on a sample of 100 observations, what is the conclusion if α = 0.10? Interpret the results at α = 0.10.