4) Test the claim given. Identify the null and alternative hypotheses, test stat

Question

4) Test the claim given. Identify the null and alternative hypotheses, test statistic, and the P-Value. Make a final conclusion and word it according to the flow chart.

Smoking and College Education

One survey showed that among 785 randomly selected subjects who completed four years of college, 18.3% smoke and 81.7% do not smoke (based on data from the American Medical Association). Use a 0.05 significance level to test the claim that the rate of smoking among those with four years of college is less than the 27% rate for the general population. Why would college graduates smoke at a lower rate than others?

Explanation / Answer

We find a 95% confidence interval for the proportion of college graduates who smoke

p = 0.183 +/- 1.96 sqrt ( 0.183 * 0.817 / 785)

= 0.183 +/- 0.0270

= ( 0.156, 0.21 )

thus, 15.6% to 21% of the college graduates smoke.

Ho : rate of smoking among college graduates < 27%

Ha : rate of smoking is >= 27%

We see that sample mean = 0.183

SE = 0.027

Thus, it could be safely stated at 0.05 level of significance that college graduates smoke at a lower level than the national average or the general population.

Hope this helps.

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