proportions The use of alcohol and tobacco by high school seniors has decreased

Question

proportions

            The use of alcohol and tobacco by high school seniors has decreased over the past 30 years. Alcohol use is down from 68.2% to 43.1%, and the use of cigarettes by high schools fell from 36.7 to 20.4% . A random sample of 300 high school seniors from a large region showed that 18% had used cigarettes during the 30 days prior to the survey. The researcher hypothesizes that the proportion of this region’s high school seniors who use tobacco is less than the national average. At = .05, is she correct? Use the P-value method, rounding to 4 digits.

Explanation / Answer

H0 : perentage of high school seniors is same or more than the national average. ptobacco = 0.204

Ha : percentage of high school seniours is less than the national average. ptobacco < 0.204

Sample size = 0.204

standard error of the proportion se0 = sqrt [p0 * (1-p0)/N] = sqrt[0.204 * 0.796/300] = 0.0233

Sample proportion p^ = 0.18

Test statistic

Z = (0.18 - 0.204)/ 0.0233 = -1.03

p - value = Pr(Z < -1.03) = 0.1515 > 0.05

so at alpha = 0.05, we shall reject the null hypothesis and can conclude that there is no decrease in the tobacco use level among high school seniors compared to national level.

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