Math 2000 Solutions 8

Fall 2001

Unit 5A

4. The population is all adult Americans; the sample is the 1200 adults selected from the population. The population parameter is the percentage of all adult Americans who respond yes/no to the question. The population parameter cannot be measured, but it will be estimated from the sample statistic. The sample statistic is percentage of those in the sample who respond yes/no to the question.

10. Step 1: The population is all people who go to restaurants; the goal is to determine average (percentage) tip left in restaurants. Step 2: Choose a representative unbiased sample, perhaps by randomly selecting 50 different customers in several different restaurants over a period of several days. Step 3: Determine average tip for those in sample. Step 4: Infer average tip for all people who east in restaurants. Step 5: Assess results; formulate conclusion.

14. The math class would be the most representative sample, as there is no obvious connection between taking a math class and one's dietary habits! The students in a single dorm would not be a representative sample, as the eating habits of these students could be quite different from those who live off campus. The public health majors or sports participants would not be representative either, as their health awareness and high energy activities, respectively, are likely to result in non-average dietary habits.

20. This is an example of simple random sampling. It's easy to automate and carry out.

24. This is an observational, case-control study; cases are participants who exercise regularly; controls are participants who do not.

30. An experimental study would be best: one group would consist of swimmers who play soccer on a regular basis, and a control group would consist of swimmers who do not play soccer.

34. The proportion of people showing improvement in the treatment group was the same as in the control group: there is no evidence that the treatment is effective.

38. The confidence interval for the percentage of voters in favor of the Democratic candidate is obtained by subtracting and adding the margin of error, namely 2%, from the sample statistic, which is 48.5%. This yields a confidence interval of 46.5% to 50.5%. Since this interval includes 50%, it is not clear that the Democratic candidate will lose the election: this one is too close to call.