Question

From generation to generation, the mean age when smokers first start to smoke varies. However, the standard deviation of that age remains constant at around 2.1 years. A survey of 39 smokers of this generation was done to see if the mean starting age is at least 19. The sample mean was 18.2 with a sample standard deviation of 1.3. Do the data support the claim at the 5% level?

Note: If you are using a Student's t-distribution for the problem, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)

1) State the distribution to use for the test. (Round your answers to four decimal places.)

2) What is the test statistic? (If using the z distribution round your answers to two decimal places, and if using the t distribution round your answers to three decimal places.)

3) What is the p-value? (Round your answer to four decimal places.)

4) Alpha (Enter an exact number as an integer, fraction, or decimal.)
α =

5) Construct a 95% confidence interval for the true mean. Sketch the graph of the situation. Label the point estimate and the lower and upper bounds of the confidence interval. (Round your lower and upper bounds to two decimal places.)

Answer 1

Solution:

Given that:

%

1) Distribution of the test is standard normal

2) Under H₀ , test statistic

  

  

3) P-value =P(Z<z)=P(Z<-2.68)

= 0.0037

If H₀ true , then these is equal to p-value that average age of people when they first begin to smoke is 18.1 year or less.

4)

p- value < , Reject null hypothesis.

i) =0.05

5) 95% Confidence interval for mean