A researcher wishes to show that the mean t of a normal popu

A researcher wishes to show that the mean .t of a normal population is greater than 20. A test is performed with alpha = 0.05. A sample of size n = 9 yields X vector = 24 and s = 6. (a) State the null and alternative hypothesis. (b) Give the rejection region. (c) Give the test value and state the conclusion. (d) Give the P-value and state the result if alpha = 0.02.

Solution

a) H0: mean=20

H1: mean>20

b) the rejection region is to the right of the mean.

c) t=2

t=xbar-mean/s/sqrt(n-1))

We reject the null hypothesis.

d) p value is 0.0403. since 0.0403 is > 0.02, we accept the null hypothesis.