(Solution) - The paper referenced in the previous exercise also gave the -(2025 Original AI-Free Solution)

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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.

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.