Diet and health have become big business,but many people are not following good health practices.In 1980,a survey of 150 indicated that 30 percent said that at least one time during that year they had five or more alcoholic drinks in one sitting.In 2000,a similar survey of 150 showed that 38 percent had five drinks in one sitting at least one time during the year.Does this represent a significant increase? Use 0.01 level of significance.

Question

Quizplus · Accepted Answer

We need to conduct a two-sample z-test for proportions to determine whether there has been a significant increase in the proportion of people who drink heavily at least one day during the year. Using a significance level of 0.01, the critical value for a two-tailed test is ±2.33. The test statistic is calculated as:

z = (p2 - p1) / sqrt(p * (1 - p) * (1/n1 + 1/n2))

where p1 is the proportion from the first survey, p2 is the proportion from the second survey, p is the pooled proportion, n1 and n2 are the sample sizes from the first and second surveys, respectively.

In this case, p1 = 0.30, p2 = 0.38, n1 = n2 = 150. The pooled proportion is:

p = (x1 + x2) / (n1 + n2) = (30 + 38) / (150 + 150) = 0.34

Plugging in the values, we get:

z = (0.38 - 0.30) / sqrt(0.34 * 0.66 * (1/150 + 1/150)) = 1.46

Since |-1.46| < 2.33, we fail to reject the null hypothesis that there has been no significant change in the proportion of those who drink heavily at least one day during the year. Therefore, the answer is C.

Diet and Health Have Become Big Business,but Many People Are