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?
The logic is correct, if the calculated value is bigger than the critical value then you reject .
The question is have you got the correct calculated value? Because you only have the standard deviation of the sample ( ) and not the population ( ) you should employ a t-test.
I.e Reject if
I have not done the workings myself, but it seems reasonable to me, if you have followed these steps you should be confident in your answer, given there are no silly arithmetic errors.
Just remember, as the sample size gets very large then
In your case the sample size is still quite small.