AP Statistics More Sampling Design Solutions 1. Modern Managed Hospitals (MMH) is a national for-profit chain of hospitals. Management wants to survey patients discharged this past year to obtain patient satisfaction profiles. They wish to use a sample of such patients. Several sampling techniques are described below. Categorize each as simple random, stratified, systematic, cluster, or convenience sample. Stratified a. Obtain a list of patients discharged from all MMH facilities. Divide the patients according to length of hospital stay (3 days or less, 3 – 7 days, 8 –14 days, more than 14 days). Draw simple random samples from each group. SRS b. Obtain lists of patients discharged from all MMH facilities. Number these patients, and then use a random number table to obtain the sample. Cluster c. Randomly select some MMH facilities from each of five geographic regions, and then survey all of these hospitals’ discharge lists. Systematic d. At the beginning of the year, instruct each MMH facility to survey every 500th patient discharged. Convenience e. Instruct each MMH facility to survey 10 discharged patients this week and send in the results. 2. From the list of people below, you want to draw an SRS of six people to survey. Using the random digits provided, who would they be? 1) Mary 2) Joe 3) Susan 4) Alice 5) Bill 6) Jose 7) Kathy 8) Herbert 9) Lucy 10) Sean 11) Howard 12) Tom 13) Gay 14) Julie 15) Neil 16) Ralph 17) Louise 18) Sam 19) Alex 20) Tanisha 21) Doug 5 3 3 4 0 7 1 5 4 6 0 5 2 3 3 5 3 9 4 6 6 8 7 4 3 7 2 4 6 0 2 7 6 0 4 5 4 0 3 8 8 6 9 2 0 7 5 1 1 8 8 9 1 5 4 1 2 6 7 1 6 8 5 3 8 4 5 6 0 0 6 9 4 0 5 9 7 7 1 9 6 6 4 6 5 4 4 1 2 0 9 0 3 6 2 3 7 1 2 2 7 2 3. Explain how to use a stratified sample design to select your survey participants in question 2. We could stratify by gender. Number the females 1 – 8, and choose 1 digit numbers until you have chosen 3. Number the males 01 – 13, and choose two digit numbers until you have chosen 3. The 3 males and 3 females make up your sample 4. A political scientist surveys 400 voters randomly selected from the list of all registered voters in a community. The purpose is to estimate the proportion of registered voters who will vote in an upcoming election. a) What is the population of interest in this survey? All the registered voters in the community b) What is the sample in this survey? The 400 voters selected c) What is the parameter of interest in this survey? The proportion of registered voters who will vote in an upcoming election 5. A supervisor is trying to improve sales at an insurance company. The supervisor asks all agents to turn in their logs from the past month, which record how much time each of them spent with individual prospective customers. The supervisor examines each agent’s average time spend with customers and the number of policies the agent sold. What kind of study is this? A) An observational study using a sample B) An observational study using a census all the logs were turned in from the past month; no treatment C) An experiment using a sample D) An experiment using a census E) A census, but whether it is an experiment or an observational study cannot be determined 6. A certain high school has 2,350 students. The student body officers are interested in creating activities to have the freshmen become more involved. Which is the best method that will give the appropriate representation of the freshmen at that school? A) During the lunch hour, ask some freshmen their choice of activities B) Take a simple random sample of the entire student body and ask their choice of activities C) Take a simple random sample of the freshmen class only and ask their choice of activities D) Take a simple random sample of non-freshmen and ask which activities they would have likes when they were freshmen. E) The student body officers should make the decision based on their experiences as freshmen. 7. In a large city school system with 20 elementary schools, the school board is considering the adoption of a new policy that would require elementary students to pass a test in order to be promoted to the next grade. The PTA wants to find out whether parents agree with this plan. Listed below are some of the ideas proposed for gathering data. For each, indicate what kind of sampling strategy is involved. Then tell whether or not you think this will result in a good, representative sample, and explain why. a) Put a big ad in the newspaper asking people to log their opinions on the PTA Web site. Convenience; not a good sample – not everyone will see the ad, all who see the ad may not go to the website b) Randomly select one of the elementary schools and contact every parent by phone. Cluster; ok if you can contact every parent; if there are many elem. schools that are very different, you might not get a representative sample c) Run a poll on the local TV news, asking people to dial one of two phone numbers to indicate whether they favor or oppose the plan. Convenience or Voluntary Response; only people who feel strongly will call, not everyone watches the news, people who call might not be parents d) Hold a PTA meeting at each of the 20 elementary schools and tally the opinions expressed by those who attend the meetings. Stratified; will probably be a pretty good sample, except the people who don’t go to the PTA meeting will not be represented e) Randomly select one class at each elementary school and contact each of those parents. Cluster; could get a pretty good sample since we’re including all the elementary schools f) Go through the district’s enrollment records, selecting every 40th parent. PTA volunteers will go those homes to interview the people chosen. Systematic; could get an okay sample, but it will be very time consuming 8. What is the purpose of stratification in sampling? A) To reduce variability in the response B) C) D) E) To increase the sample size To restrict which members of the population can be sampled To reduce response bias To ensure an equal probability of a particular individual being sampled 9. The student council wants to survey students at the school to see what brands of soda pop they want in the school machines. They randomly sampled 30 freshmen, 30 sophomores, 30 juniors, and 30 seniors. The sampling method they used is a A) Simple random sample B) Stratified random sample D) Systematic random sample E) Convenience C) Cluster sample 10. Suppose your local school district decides to randomly test high school students for attention deficit disorder. There are three high schools in the district, each with grades 9-12. The school board pools all of the students together and randomly samples 250 students. Is this a simple random sample? A. Yes, because the students were chosen at random B. Yes, because each student is equally likely to be chosen C. Yes, because they could have chosen any 250 students form throughout the district D. No, because we can’t guarantee that there are students from each school in the sample E. No, because we can’t guarantee that there are students from each grade in the sample
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