From generation to generation the mean age when smokers firs

From generation to generation, the mean age when smokers first start to smoke varies. However, the standard deviation of that age remains constant of around 2.1 years. A survey of 40 smokers of this generation was done to see if the mean starting age is at least 19. The sample mean was 18.1 with a sample standard deviation of 1.3. Do the data support the claim at the 5% level?

Solution

Set Up Hypothesis
Null,the mean starting age is at least 19 H0: U>=19
Alternate, H1: U<19
Test Statistic
Population Mean(U)=19
Sample X(Mean)=18.1
Standard Deviation(S.D)=1.3
Number (n)=40
we use Test Statistic (t) = x-U/(s.d/Sqrt(n))
to =18.1-19/(1.3/Sqrt(39))
to =-4.379
| to | =4.379
Critical Value
The Value of |t | with n-1 = 39 d.f is 1.685
We got |to| =4.379 & | t | =1.685
Make Decision
Hence Value of | to | > | t | and Here we Reject Ho
P-Value :Left Tail -Ha : ( P < -4.3785 ) = 0.00004
Hence Value of P0.05 > 0.00004,Here we Reject Ho

We don\'t have evidence to indicate that the mean starting age is at least 19