12.8 The paper referenced in the previous exercise also gave the accompanying data on the age at which smoking started for a sample of 1031 men who smoked low-tar cigarettes.

Age Frequency

16 237 16–17 258 18–20 320

21 216

a. Use a chi-square goodness-of-fit test to test the null hypothesis H0: p1  .25, p2  .2, p3  .3, p4  .25, where p1  proportion of male low-tar cigarette smokers who started smoking before age 16, and p2, p3, and p4 are defined in a similar way for the other three age groups.

b. The null hypothesis from Part

(a) specifies that half of male smokers of low-tar cigarettes began smoking between the ages of 16 and 20. Explain why p2  .2 and p3  .3 is consistent with the ages between 16 and 20 being equally likely to be when smoking started.