1. In a recent study on SIDS (Sudden Infant Death Syndrome), one hospital collected data on 128 babies who died from SIDS. They then took a random sample of 500 babies who did not die from SIDS, and they compared the two groups with respect to several variables (e.g. did the child sleep on his/her stomach, birth weight, time of year, whether the mother smoked, whether she breast- fed, etc.). One physician noted that 63% of the SIDS babies had mothers that smoked during pregnancy, whereas only 26% of the control babies had mothers who smoked during pregnancy.
From this evidence, can we conclude that smoking during pregnancy is a likely cause of SIDS in babies? Explain, and give a concrete example.
2. In 1948 the pollster George Gallup used something called quota sampling to (incorrectly) predict that Thomas Dewey would beat Harry Truman in the presidential election. [In quota sampling a population is first segmented into mutually exclusive sub-groups or strata, just as in stratified random sampling, then judgment is used to select the subjects or units from each segment].
Discuss the problem with the approach to sampling taken by Gallup.
3. Recently Ed Schultz, a political contributor for MSNBC, polled his audience on the "Ed Show" asking:
Are the increasing gas prices the fault of President Obama? The results of the cell phone poll were as follows: Yes--12%; No--88%.
What are the biases that this poll is subject to?
4. Consider a population of N = 5 units, labeled A, B, C, D, E. Consider a simple random sampling design with a random size n = 3.
a. List every possible sample of size n = 3.
b. If this population is sampled using simple random sampling, what is the probability that the sample {A,B,C} will be selected?
5. We wish to conduct a survey to estimate the proportion, p, of individuals in the population who have tested positive for HPV. A simple random sample of 1000 individuals is chosen. Each person is then supplied with a coin and given the following instructions: Flip the coin in secret, if the coin comes up heads, answer question A below. If it comes up tails, answer question B.
Question A: To your knowledge, are you infected with HPV?
Question B: Is your zodiac sign included in the following set? {Cancer, Leo, Virgo} Of the 1000 sampled individuals, suppose 170 respond "Yes."
a. How many people would expect to answer A, and how many would you expect to answer B?
b. Of the people who answered B, how many people would you expect to answer "yes"?
c. Using you answer to (b) estimate the percentage, p, of people in the population that are carriers of HPV and are aware of their condition?