STAT 100 Fall 2014 Midterm 1 VERSION B

Transcription

1 STAT 100 Fall 2014 Midterm 1 VERSION B Instructor: Richard Lockhart Name Student Number Instructions: This is a closed book exam. You may use a calculator. It is a 1 hour long exam. It is out of 30 marks in total. QUESTION 1 [2 marks in total] Multiple choice questions: choose the best answer from each list. No explanation is required. [1 mark each] A. Bias in a sampling method is d a. Accounted for by the margin of error. b. A consequence of random variation. c. An error that would be different if you reran the survey the same way on the same population. d. An error that is systematic and tends to move the results the same way every time you use the sampling method. B. Which of the following is not true about the margin of error for a simple random sample of size 1000 chosen from a population of size 4,000,000? b a. It is smaller than it would be if I decreased the sample size to 500. b. It would be bigger if the sample size were the same but the population size were 10,000,000. c. It is unaffected by response bias. d. It is bigger than it would be if I increased the sample size to 4000

2 QUESTION 2 [Total of 6 marks] Nanos Research is a Canadian polling company. In August of 2014 they carried out a survey that they describe in the following way: National Nanos conducted a RDD [Random Digit Dialing] dual frame (land- and cell-lines) hybrid telephone and online random survey of 1,000 Canadians between August 24th and 28th, Participants were randomly recruited by telephone and administered a survey online. The results were statistically checked and weighted by age and gender using the latest Census information and the sample is geographically stratified to be representative of Canada. Individuals [were] randomly called using random digit dialling with a maximum of five call backs. The margin of error for a random survey of 1,000 Canadians is ±3.1 percentage points, 19 times out of 20. For each of the following issues write one sentence to say whether or not it is a potential problem with this survey and why? [So your answer might be this is not a problem because this is a census or this is a problem because the question is asked in a way which encourages people to say yes or there is no clear information about this in the description.] 2 Marks each. A. Undercoverage I think that almost everyone has a cell phone or a land line so I would say this is not likely to be a big problem B. Overcoverage. I think this is likely to be a problem because there are lots of people who have both a cell phone and a land line. C. Non-response bias. This is likely to be an issue. The sentence about a maximum of five call backs suggests that a number of people were called multiple times without success. Experience also shows that refusals are now quite common. 2

3 QUESTION 3 [total of 6 marks] In the survey described in the previous question a total of 530 people agreed with the statement We need more women elected in our democracy. [They were also allowed to say they agreed somewhat, disagreed somewhat, disagreed or were unsure.] a) Estimate the proportion of Canadians who agree with the given statement. [2 marks] 530/1000 is 53%. b) Provide a confidence interval for this proportion using the information given. [2 marks] The MOE will be 100% times 1/sqrt{1000} =3.1% and the confidence interval runs from 53%-3.1% to 53%+3.1% or 49.8% to 56.1%. c) This confidence interval does not account for all the sources of error in this survey. Name two sources of error that are not accounted for by this confidence interval. [2 marks] Confidence intervals do not account for non-response bias, nor for overcoverage. They don t account for response bias or undercoverage either but these are not likely problems in this survey. QUESTION 4 [3 marks] Nanos says The results were statistically checked and weighted by age and gender using the latest Census information and the sample is geographically stratified to be representative of Canada. Why did they weight the results using Census information? [3 marks] Weighting serves two purposes. In surveys where it is not mandatory to reply the weighting helps decrease the non-response bias. I told you in class that it also decreases the sampling variability of the estimates because it adjusts the sample to have similar age and sex distributions to that of the population. 3

4 QUESTION 5 [10 marks in total] For its 50 th Anniversary Simon Fraser University would like to survey its alumni to find out how they feel about their time at SFU after having been out of school for a while. There are about 100,000 graduates of SFU stretching back to the 1960s. The university chooses a simple random sample and goes through their records to get addresses and phone numbers. They mail their survey out and get responses back from 400. A. What was the population for the study? [1 mark] The collection of all SFU graduates. B. One question was, Do you feel that your degree prepared you well for the job market? A total of 260 respondents answered Yes. a. Estimate the percentage of the population that feels that the their degrees prepared them well for the job market. [1 mark] 100% x 260/400 = 65% b. Find the margin of error for the estimate. [1 mark] 1/sqrt{400} = 0.05=5% c. Explain what the margin of error tells you about the population here. [1 mark] If sampling error were the only kind of error in this survey we would be confident (95% confident) that between 55% and 65% of all graduates would say Yes to this question. The bias problem I am worried about is dealt with in D. 4

5 C. Imagine the university decides that 260 out of 400 is too low and launches an internal review to make programs more relevant to the job market. Five years later they carry out another survey of about the same size surveying only those who graduate in that 5-year period. Imagine they asked the same question and got an estimate that was statistically significantly lower than the current estimate. Can the university claim that the internal review has been successful? Explain. [2 marks] Other things will almost certainly have changed in the interval. The job market for recent grads was different than for old grads for instane. Too, the new survey covers only recent grads and they are being compared to a group of grads many of whom were not at all recent grads at the time of the first survey. So there will be differences between the groups that have nothing to do with the internal review. D. One of the following is likely to be a big problem for this survey: non-response bias, response bias, overcoverage, sampling variability. Say which one and explain why. Also pick one that is not likely to be a big problem and say why. [4 marks] Non-response bias is likely very important. The university likely had to try to contact many more to get 400 reponses and they will have had a great deal of difficulty contacting older alumni and those who left Vancouver after graduating. Overcoverage is probably not a problem the university has a very good list of its alums. Response bias is not likely to be a big problem. The question wording is clear and not controversial. 5

6 QUESTION 6 [total of 3 marks] The table below lists average grades for a variety of departments at the upper and lower division level over the course of several years. Imagine we are studying grades to determine the extent to which the level of the course and the type of course influences how high the grades are. Academic Year Course Code Division Average GPA Number of Students 2010/11 Criminology Lower /12 Criminology Lower /13 Criminology Lower /14 Criminology Lower /11 Criminology Upper /12 Criminology Upper /13 Criminology Upper /14 Criminology Upper /11 Education Lower /12 Education Lower /13 Education Lower /14 Education Lower /11 Education Upper /12 Education Upper /13 Education Upper /14 Education Upper /11 Statistics Lower /12 Statistics Lower /13 Statistics Lower /14 Statistics Lower /11 Statistics Upper /12 Statistics Upper /13 Statistics Upper /14 Statistics Upper A. List any response variables: Average GPA B. List any explanatory variables: Course Code and Division C. Select any variable and list its values: Division: Lower and Upper; others are possible of course. 6