AP Statistics!!! Test Review 2013 Sampling Error ◦ Occurs in the act of choosing the sample ◦ Undercoverage – certain members of population are ‘left out’ Suppose we use poll people a group of people at a golf tournament about how they feel about the Affordable Care Act… Non Sampling Error ◦ Occurs after sample is chosen ◦ Non response – cannot be surveyed or refuse to answer question. ◦ Response Bias ◦ Poorly Worded Questions Which type of error is made when you use phone calls to sample people, but you call during working hours? ◦ Answer: Non Response (non sampling error) Which type of error is made when you use a telephone to sample people? ◦ Answer: Undercoverage (sampling error) What type of error is shown below: ◦ Question: “How do you feel that the extremely expensive Affordable Care Act will help your and your family’s overall health and wellness?” ◦ Answer: It is a poorly worded question (nonsampling error) and will UNDERESTIMATE the support for the A.C.A. Voluntary Response Sample ◦ Participants ‘choose’ or volunteer themselves (not random; very biased) Convenience Sample ◦ We only include who is ‘convenient’ to survey. (not truly random; biased) Simple Random Sample (SRS) ◦ Every person has an equal chance to be selected (“all the names are in ‘one pot’”) DO NOT BREAK INTO GROUPS!!! Stratified Random Sample ◦ Population is divided into groups or ‘strata’ that are made up of similar individuals within each group. You do an SRS within each group. Systematic Sample ◦ We sample every ‘kth’ person after the first person is randomly selected. Multi-Stage Sample ◦ Done on a large scale; combining other types of sampling methods; you sample to choose GROUPS, then sample within the groups. Cluster Sample ◦ Population is divided into groups that don’t necessarily all look alike; the clusters should ‘mirror the population; you sample to choose GROUPS, then take a census within the group. Review of Chapter 4 Vocab Simple Random Samples (“chopping through #’s) ◦ Labels 9 people? 10 people? 100 people? 57 people? 124 people? You have two dogs, each of whom have a litter of 12 puppies. You want to determine the amount of weight gain over 12 weeks based on the type of food you give them. If you give puppy food #1 to one dog’s 12 puppies and puppy food #2 to the other dog’s 12 puppies and then compare the weight gain after 12 weeks, what type of experiment have you carried out? ◦ Answer: An experiment, but NOT completely randomized Puppies… continued… Suppose you now give puppy food #1 to an SRS of 6 puppies from one ‘momma dog’ and an SRS of 6 puppies from the other ‘momma dog’, with the remaining 12 puppies from the two ‘momma dogs’, then what type of design have you used now? ◦ Answer: Block Design, based on which ‘momma dog’ Explain Double-blind experiments …. Single-blind… Suppose that you decide to do a survey in Somerset to inquire about a ‘particular issue’. You decide to select an SRS of 50 homes in the city limits and you contact them for a face-to-face interview that consists of 2 questions. What is the chance that all 50 homes just happened to be drawn from the same neighborhood (Oaklawn)? ◦ Answer: the same chance as for any other set of 50 homes…. S You wish to do a survey of residents in the state of Tennessee. You select an SRS of 100 adults heads of households in each county in the state and ask their opinion on the selected topic. What type of sample is this? ◦ Answer: Stratified Does the amount of sales of ice cream (in dollars) accurately predict the number of drowning's in Lake Michigan? Does ice cream CAUSE drownings? Consider what conclusion can be drawn? ◦ Answer: Lurking/confounding variable – seasonal variation in temperature… hotter it is, more ice cream consumed…. More people swim…. Thus, more drownings… An experiment will take place at Kroger, in which participants will taste test each of two kinds of sweet tea. What type of design is this? ◦ Answer: Matched Pairs I choose to do a survey at Somerset High School. I randomly select 2 homerooms per grade and ask every student in those homerooms the selected question. What type of sample is this? ◦ Answer: Cluster… (sample, then census) I decide to do a large-scale sample using Gallup. I want to gather information about feelings about a potential major candidate for the U.S. presidency. I then select 10 states, and then within those 10 states, I select 2 AREA CODES and then select 200 people randomly from those AREA CODES to be a part of the survey… What type of sample is this? ◦ ANSWER: Multi-stage I decide to do a survey at the University of Alabama. I decide to divide the student population into groups based on the following criteria ◦ In state and in what 5 different regions from AL they are from ◦ Out-of-state ◦ I then do random samples within each of the 6 groups. ◦ What type of sample have I done? ◦ ANSWER: Stratified Why is doing an SRS of 100 people preferable to doing an SRS of just 10 people? At a certain university, students who live in dormitories eat at a common dining hall. Recently, some students have been complaining about the quality of the food service there. The dining hall manager decides to do a survey to estimate the proportion of students living in the dormitories who think the quality of food should be improved. One evening, the manager asked the first 100 students entering the dining hall to answer the following question: Many students believe that the food served in the dining hall needs improvement. Do you think that the quality of food services here needs improvement, even though that would increase the cost of the meal plan? _____ Yes _____ No ______ No Opinion. FRAPPY #1: ‘DORM FOOD’ a. In this setting, explain how bias may have been introduced based on the way this convenience sample was selected and suggest how the sample could have been selected differently to avoid that bias. a. In this setting, explain how bias may have been introduced based on the way the question was worded and suggest how it could have been worded differently to avoid that bias. Questions… INTENT: Measures student knowledge of: ◦ How bias affects sample selection. ◦ How wording of question affects sample results. Scoring Criteria: ◦ Part a: Must correctly explain how this type of sampling method will introduce bias. Must create a better sampling method that would avoid/lessen bias. ◦ Part b: Must explain how the wording of the question introduced bias. Must offer a better way to word the question. SCORING CRITERIA & INTENT Part a: ◦ The issue is that the first 100 people who enter the dining hall are likely individuals who like the food the most, simply because they are there and are FIRST to be in line. ◦ ANSWERS must show a better design (RANDOM); but should not simply resort to a census or a ‘better’ convenience sample. “I would have a dining hall employee hand a survey to every 10th person who is line all day long and ask them to answer the question.” “I would do a stratified sample of all the dorms on campus. Within each dorm randomly select rooms based on their assigned room number and ask them the question.” Model Solution Part b: ◦ TWO WAYS OF LOOKING AT IT… The question is a ‘leading question’ in that it suggests that other students have already expressed there disapproval of the food in the dining hall, which would make students chooses ‘yes’ The question also suggest rising costs of the meal plan, which would cause students to answer ‘no’ ◦ BETTER WAY: “It would be best to leave out the part stating how other students feel and the part about the increase in costs and just ask: “Do you think the quality of food services here needs improvement?” Model Solution An apartment building has nine floors and each floor has four apartments. The building owner wants to install new carpeting in eight apartments to see how well it wears before she decides whether to replace the carpet in the entire building. AP Statistics – Chapter 4 FRAPPY Practice #4 2011 AP Statistics Exam Question #3 The figure below shows the floors of apartments in the building with their apartment numbers. Only the nine apartments indicated with an asterisk (*) have children in the apartment. a. For convenience, the apartment building owner wants to use a cluster sampling method, in which the floors are clusters, to select the eight apartments. Describe a process for randomly selecting eight different apartments using this method. b. An alternative sampling method would be to select a stratified random sample of eight apartments, where the strata are apartments with children and apartments with no children. A stratified random sample of size eight might include two randomly selected apartments with children and six randomly selected apartments with no children. In the context of this situation, give one statistical advantage of selecting such a stratified sample as opposed to a cluster sample of eight apartments using the floors as clusters.