3. A random sample of 8 cigarettes of a certain brand has an average nicotine content of 4.2 mg and a standard deviation of 1.5 mg. Is this in line with the manufacturer’s claim that the average...

3. A random sample of 8 cigarettes of a certain brand has an average nicotine content of 4.2 mg and a standard deviation of 1.5 mg. Is this in line with the manufacturer’s claim that the average nicotine content does not exceed 3.5 mg. Use a 0.05 level of significance. Assume the distribution of nicotine contents to be normal.

4. A study was made to estimate the difference in salaries of college professors in the private and state colleges of North Carolina. A random sample of 100 professors in private

colleges showed an average 9-month salary of $ 32,000 with a standard deviation of $1,300. A random sample of 200 professors in state colleges showed an average of $32,900 with a standard deviation of $1,400. Test the hypothesis that the average salary for professors teaching state colleges does not exceed the average salary for professors teaching in private colleges by more than $500. Use a 0.01 level of significance.