Hypothesis Test . Distribution

Oct 2019
united states
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 43 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?

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.)

a) State the distribution to use for the test. . I used

x-N (18.1, .3507) . I divided 2.1 for the square room of 43. But give wrong. What I am doing wrong?