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 of39smokers of this generation was done to see if the mean starting age is at least 19. The sample mean was18.2with a sample standard deviation of 1.3. Do the data support the claim at the 5% level?

Note: If you are using a Student'st-distribution for the problem, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)

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

What is the test statistic? (If using thezdistribution round to two decimal places, and if using thetdistribution round to three decimal places.)

What is thep-value? (Round to four decimal places.)

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.)