Sampling Design Homework

AP Statistics Review Sampling Design Homework

1-3 Identify the population in the study, the sample, and the sampling method (include whether it was random or not. 1. A sociologist wants to know the opinions of employed adult women about government funding for day care. She obtains a list of the 520 members of a local business and professional women’s club and mails a questionnaire to 100 of these women selected at random. Only 48 questionnaires are returned. Population: ALL employed adult women in the world Sample: 48 women from local businesses and a professional women’s club Sampling method: Cluster sampling utilizing a voluntary response Randomization: Voluntary response is not random sampling method….it creates bias (only the truly passionate will respond), and this style of clustering creates undercoverage (blue collar employed workers are left out).

2. A business magazine mailed a questionnaire to the human resources directors of all of the Fortune 500 companies, and received responses from 23% of them. Those responding reported that they did not find that such surveys intruded significantly on the workday. Population: Human resource directors for fortune 500 companies Sample: 23% of the HR directors Sampling Method: Voluntary response through survey Randomization: none…..voluntary response are extremely biased.

3. Researches waited outside a bar they had randomly selected from a list of such establishments. They stopped every 10th person who came out of the bar and asked whether he or she thought drinking and driving was a serious problem. Population: Difficult to determine…..but assumed that it is people who drink in bars Sample: Every 10 person exiting the bar (what is the age range (21 and up). What do we know about these bars….what city are they in (a college town, uptown Houston, Deep Elm in Dallas0 Sampling method: Cluster method paired with systematic random Randomization: The method within this study was randomly design the sample that was selected….however, there was serious undercoverage because only people who go to bars were surveyed in regard to the serious problem associated with drinking and driving. A truly random experiment would have questioned all individuals aged 21 and up or whatever the actual population of this study should be

4. Describe how you would select a sample of 30 juniors from your school using the following methods:

a. SRS: random # generator……selecting from the entire junior class.

b. Stratified random sampling: There are a great number of possible scenarios here: Here is one example: Divide the Juniors up based off of their GPA (91-100), (81-90), (71-80), (61-70)…..the number the juniors within each group, and use a random number generator to select the same number from each group. You could break them into groups by extra-curricular’s, hair color, ethnicity, etc.

You would need to make sure that whatever groups you make have similar sizes. So for my example above, I may have to rework the splits to ensure group size.

c. Convenience sampling Stand in the hall way, and pick the first 30 juniors that walk past you.

d. Voluntary response sampling Make an announcement asking for 30 volunteers from the junior class

e. Systematic sampling Take a printout of the entire junior class. Take the total number of people and divide it by 30. Use a number generator to pick a number a number from 1 to that number, and then add that number to it each time.

5. Some medical researchers suspect that added calcium in the diet reduces blood pressure. You have available 40 men with high blood pressure who are willing to serve as subjects. You want to give 8 men the calcium additive and the rest a placebo (sugar pill). In an experiment, you need to randomly allocate the subjects as specified above. Technically, this is not a simple random sample, but the random allocation works the same.

a) The names of the subjects appear below. List the subjects to whom you will give the drug. (use the given random #’s). Mark clearly on the number line indicating your selections. Start by numbering them

1 Alomar 9 Denman 17 Han 25 Liang 33 Rosen 2 Asihiro 10 Durr 18 Howard 26 Maldonado 34 Solomon 3 Bennett 11 Edwards 19 Hruska 27 Marsden 35 Tompkins 4 Bikalis 12 Farouk 20 Imrani 28 Moore 36 Townsend 5 Carlson 13 Furgeson 21 James 29 O’Brian 37 Troy 6 Chen 14 George 22 Kaplan 30 Ogle 38 Underwood 7 Cranston 15 Green 23 Krushchev 31 Pittman 39 Willis 8 Curtis 16 Guillen 24 Lehman 32 Rodriguez 40 Zhang

42672 67680 42376 95023 82744 03971 96560 55148 26461 88346 52430 60906 74216

b) As mentioned above, since this scenario was an experiment, we used random allocation as oppose to a simple random sample (even though they worked very similar). Explain why the process above cannot be called a simple random sample. Not every individual has the same probability of being selected since only 8 individuals will get the treatment, and the remaining 32 will be the placebo Circle the best answer. Explain briefly why each answer was correct or incorrect. 6. Suppose that a number of crates of pencils is chosen at random from a boxcar of crates, and then a number of boxes of pencils is chosen at random from each selected crate. Our goal is to determine the number of defective pencils in a box. This is an example of…

A) simple random sampling

B) multi-stage sampling

C) stratified sampling

D) systematic sampling

E) none of the above

7. The following is a map of a census tract in a fictitious town. Census tracts are small, homogeneous areas averaging 4000 in population. On the map, each block is marked with a Census Bureau identification number. A random sample of blocks from a census tract is often the next-to-last stage in a multistage sample. Explain how you will set up a simple random sample of 5 blocks from this census tract using their identification numbers. Be sure to mark clearly on the number line and explain what happens with unused numbers.

97971 48932 45792 63993 95635 28753 46069 84635 49345 183058 76213 82390 77412 Utilize these number to select the 5 blocks that you will use…the rest will be untested. 8. A club has 30 student members and 10 faculty members. The club can send 4 students and 2 faculty members to a convention. It decides to choose those who will go by random selection. Use the numbers below to choose a stratified random sample of 4 students and 2 faculty members.

STUDENTS 1 Abel 7 Fisher 13 Huber 19 Miranda 25 Reinmann 2 Carson 8 Ghosh 14 Jimenez 20 Moskowitz 26 Santos 3 Chen 9 Griswold 15 Jones 21 Neyman 27 Shaw 4 David 10 Hein 16 Kim 22 O’Brian 28 Thompson 5 Deming 11 Hernandez 17 Klotz 23 Pearl 29 Utts 6 Elashoff 12 Holland 18 Liu 24Potter 30 Varga

FACULTY 1 Andrews 3 Fernandez 5 Kim 7 Moore 9 West 2 Besicovitch 4 Gupta 6 Lightman 8 Phillips 10 Yang

487477659532588383928442280016378908099352010 719502249400369512698707373694977512388273613 178575235221392229304377610503582495764847051

You could start back over for the faculty or continue forward….both random…I continued forward

In the following description of an experiment, there is information that you have not been given. Your job is to identify the parts of the experiment, and justify your responses. Where you have not been given enough information to answer the question, you can either 1.) make an assumption, which you justify, or 2.) give two scenarios, and tell which one you think would be better. You may want to use the More On Experimental Units handout to help you. Bachman, Herzberg, and Rich conducted a factorial study of fluid flow through thin tubes. They measured the time required for the liquid level in a fluid holding tank to drop from 4 in. to 2 in. for two drain tube diameters and two fluid types. Two different technicians did the measuring. Here is their data:

Technician Diameter (in.) Fluid Time (sec) 1 .188 water 21.12, 21.11, 20.80 2 .188 water 21.82, 21.87, 21.78 1 .314 water 6.06, 6.04, 5.92 2 .314 water 6.09, 5.91, 6.01 1 .188 ethylene glycol 51.25, 46.03, 46.09 2 .188 ethylene glycol 45.61, 47.00, 50.71 1 .314 ethylene glycol 7.85, 7.91, 7.97 2 .314 ethylene glycol 7.73, 8.01, 8.32

1. What is the response variable? Time (in seconds) required for the liquid level to drop from 4in to 2in 2. How many factors? 2 factors: I am assuming that the researchers are not interested in the effect of the variable “technician” on the value of the response variable, and I am assuming that “technician” is a blocking variable. There are times, however, when we are interested in the effect of “person” on a response. For example, suppose there was an experiment where one factor was “surgeon,” with levels Dr. Brown, Dr. Jones, Dr. Smith, and another factor was “method of performing surgery”, with levels A, B, C. Suppose the response variable is “ two‐year survival rate.” Over the next year, each of the three heart surgeons in General Hospital performs heart surgery using each of the three methods, and each patient is observed for two years after surgery, whereupon his/her survival status is noted. Such an experiment is ethical if we truly do not know which method is the best and which surgeon is the best. If you are a potential patient, or if you are the person evaluating the performance of the surgeons, you are interested in the effect of surgeon on survival rate. (Yes, there are lots of complications with this experiment that I am not discussing.) 3. What are the factors (and their levels)? Diameter in inches(.188, .314) Liquid (water, ethylene glycol) 2 4. How many treatments? 4 treatments 5. What are the experimental units? There is not enough information to answer this question. Scenario 1 (Detroit): If the researchers are interested in generalizing to all tubes of this type with the two diameters and if they are interested in generalizing to any water of ethylene glycol speciments, then they need to replicate the tubes and they need to use different water and different ethylene glycol in each run of the experiment. In this case, the experimental units are specific tubes used in conjunction with specific samples of liquid. This scenario is most likely to be the scenario of interest. Scenario 2 (Detroit and NASCAR): If the researchers are interested in future drainings of water and ethylene glycol through these specific tubes, but generalized over any quantity of water or ethylene glycol (not the same water and glycol over and over), then they need to replicate the liquid samples, and the experimental unit is liquid sample. Scenario 3 (NASCAR only): If the researchers are interested in draining the same quantity of water and the same quantity of ethylene glycol over and over using the same tubes—and no, it is not likely that anyone would be interested in this—then they simply replicate the act of draining, and the experimental unit is the act of draining. 6. Are there any controlled variables? Should there be? “Person draining” should either be a controlled or a blocking varaible. The text said “person measuring” was spread over two people, but it didn’t say anything about “person draining.” All conditions under which the draining takes place should be controlled—the starting condition of the drains, the exact way the liquid is poured, the temperature, etc… 7. Are there any blocking variables? Should there be? Technician is a blocking variable. Yes, technician should be a blocking variable (or a controlled variable). See controlled variables. 8. How many replicates? They used r=3 replicates per treatment.