Discussion:
Q1) A random sample n=40 observations from a population produced a mean of 30.9 and a standard deviation of 2.4. Suppose that you wish to show that the population mean exceeds 30.
A) Give the null and alternative hypothesis for the test.
B) If you wish your probability to be of (erroneously) deciding that μ>30, when in fact μ =30, to equal 0.05, what is the value of for the test?
C) Glance at the data and use your intuition to decide whether the sample mean, 30.9 implies that μ>30 . (Do not conduct the statistical test). Now test the null hypothesis. Do the data provide sufficient evidence to indicate that μ>30? Test using α =0.05.
Q2) Refer to the problem above. Suppose that you wish to detect a value of μ that differs from 30; that is, a value of μ either greater or less than 30. State the null and alternative hypothesis for the test.