1. An environmental group conducted a study to determine whether crows in a certain region were ingesting food containing unhealthy levels of lead. A biologist classified lead levels greater than 6.0 parts per million (ppm) as unhealthy. The lead levels of a random sample of 23 crows in the region were measured and recorded. The data are shown in the stemplot below.
(a) What proportion of crows in the sample had lead levels that are classified by the biologist as unhealthy?
(b) The mean lead level of the 23 crows in the sample was 4.90 ppm and the standard deviation was 1.12 ppm.Construct and interpret a 95 percent confidence interval for the mean lead level of crows in the region.
2. An administrator at a large university wants to conduct a survey to estimate the proportion of students who are satisfied with the appearance of the university buildings and grounds. The administrator is considering three methods of obtaining a sample of 500 students from the 70,000 students at the university.
(a) Because of financial constraints, the first method the administrator is considering consists of taking a convenience sample to keep the expenses low. A very large number of students will attend the first football game of the season, and the first 500 students who enter the football stadium could be used as a sample.Why might such a sampling method be biased in producing an estimate of the proportion of students who are satisfied with the appearance of the buildings and grounds?
(b) Because of the large number of students at the university, the second method the administrator is considering consists of using a computer with a random number generator to select a simple random sample of 500 students from a list of 70,000 student names. Describe how to implement such a method.
(c) Because stratification can often provide a more precise estimate than a simple random sample, the third method the administrator is considering consists of selecting a stratified random sample of 500 students. The university has two campuses with male and female students at each campus. Under what circumstance(s) would stratification by campus provide a more precise estimate of the proportion of students who are satisfied with the appearance of the university buildings and grounds than stratification by gender?
3. Each full carton of Grade A eggs consists of 1 randomly selected empty cardboard container and 12 randomly selected eggs. The weights of such full cartons are approximately normally distributed with a mean of 840 grams and a standard deviation of 7.9 grams.
(a) What is the probability that a randomly selected full carton of Grade A eggs will weigh more than 850 grams?
(b) The weights of the empty cardboard containers have a mean of 20 grams and a standard deviation of 1.7 grams. It is reasonable to assume independence between the weights of the empty cardboard containers and the weights of the eggs. It is also reasonable to assume independence among the weights of the 12 eggs that are randomly selected for a full carton.
Let the random variable X be the weight of a single randomly selected Grade A egg.
i) What is the mean of X ?
ii) What is the standard deviation of X ?
4. The Behavioral Risk Factor Surveillance System is an ongoing health survey system that tracks health conditions and risk behaviors in the United States. In one of their studies, a random sample of 8,866 adults answered the question “Do you consume five or more servings of fruits and vegetables per day?” The data are summarized by response and by age-group in the frequency table below.
Do the data provide convincing statistical evidence that there is an association between age-group and whether or not a person consumes five or more servings of fruits and vegetables per day for adults in the United States?
5. Psychologists interested in the relationship between meditation and health conducted a study with a random sample of 28 men who live in a large retirement community. Of the men in the sample, 11 reported that they participate in daily meditation and 17 reported that they do not participate in daily meditation.
The researchers wanted to perform a hypothesis test of
where Pm is the proportion of men with high blood pressure among all the men in the retirement communitywho participate in daily meditation and Pc is the proportion of men with high blood pressure among all the men in the retirement community who do not participate in daily meditation.
(a) If the study were to provide significant evidence against Ho in favor of Ha , would it be reasonable for the psychologists to conclude that daily meditation causes a reduction in blood pressure for men in the retirement community? Explain why or why not.
The psychologists found that of the 11 men in the study who participate in daily meditation, 0 had high blood pressure. Of the 17 men who do not participate in daily meditation, 8 had high blood pressure.
(b) Let ˆPm represent the proportion of men with high blood pressure among those in a random sample of 11 who meditate daily, and let ˆPc represent the proportion of men with high blood pressure among those in a random sample of 17 who do not meditate daily. Why is it not reasonable to use a normal approximation for the sampling distribution of Pˆm-Pˆc ?
Although a normal approximation cannot be used, it is possible to simulate the distribution of ˆPm-ˆPc . Under the assumption that the null hypothesis is true, 10,000 values of ˆPm-ˆPc were simulated. The histogram below shows the results of the simulation.
(c) Based on the results of the simulation, what can be concluded about the relationship between blood pressure and meditation among men in the retirement community?
SECTION II, Part B部分