Question

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?

Answer 1

= 19, =2.1, n= 40, = 18.1, = 5% = 0.05

Ho : ≥ 19

Ha : < 19

population standard deviation is known

hence we are performing z test for normal distribution.

now calculate test statistics

z = –2.71

test statistics= –2.71

now calculate P-Value for left tailed test

P-Value = P(z < -2.71)

find P(z < -2.71) using normal z table

we get

P(z < -2.71) = 0.0034

P-Value = 0.0034

Decision:

since (P-Value= 0.0034) < ( =0.05 )

hence,

Null hypothesis is rejected.

conclusion:

Therefore there is not sufficient evidence to support the claim that the  mean age of smokers

start smoking s at least 19 years.