A recent study stated that if a person smoked, the average of the number of

cigarettes he or she smoked was 14 per day. To test the claim, a researcher

selected a random sample of 40 smokers and found that the mean number of

cigarettes smoked per day was 18. The standard deviation of the sample was 6. At

0.05(alpha), is the number of cigarettes a person smokes per day actually different

from 14?

Here's my work:

H(0): mean = 14 and H(1): mean =/= 14

z-test for the mean.

i used, 1.65 as the line. and used the equation: z = (X-mean)/(st.d / sqrt(n)).

so i got, (18-14)/(6/sqrt(40)) = 4.22.... which would reject the hypothesis. Am I

doing this right?