Cigarette companies advertise that the mean amount of nicotine in each cigarette is
1.4 milligrams. A health advocacy group believes that the amount of nicotine is
greater than the advertised amount. They hire a consultant who collects a sample of size 31 and finds that it has a mean of 1.58 milligrams with a standard deviation of
0.17 milligrams.
Run a full hypothesis test at the 1% level of significance to test the health advocacy group’s claim.
Is it necessary for the amount of nicotine in cigarettes to be normally distributed in order to run the hypothesis test? Explain your answer briefly