Answers to E, F, G and H. Practice Exam Questions

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1 Answers to E, F, G and H Practice Exam Questions E1. An experimenter is studying the bonding strength of adhesives that contain varying amounts of a particular chemical additive. Wafers of a specified material are glued together using the adhesive with each amount of additive, allowed to cure for 24 hours, and then the strength needed to separate the wafers is determined. It is reported that the correlation between the correlation between strength required and amount of additive was 0.86 pounds-force per square inch. Fill in the blanks. This report commits a major because correlation is. error, unitless. E2. As Swiss cheese matures, a variety of chemical processes take place. The taste of matured cheese is related to the concentration of several chemicals in the final product. In a study of cheese in a certain region of Switzerland, samples of cheese were analyzed for lactic acid concentration and were subjected to taste tests. The numerical taste scores were obtained by combining the scores from several tasters. A scatterplot of the observed data is shown below.

2 What is a plausible value for the correlation between lactic acid concentration and taste rating? (i) (ii) 0.7 (iii) 0.07 (iv) 0. 7 The answer is (ii). There is a moderately strong positive correlation.

3 E4. The length and width for a sample of products made by a certain company are plotted below: The correlation between length and width is calculated to be r (a) In the plot, notice that length is treated as the response variable and width as the explanatory variable. Suppose we had taken width to be the response variable and length to be the explanatory variable. What would be the correlation between width and length in this case? (i) (ii) (iii) (iv) Any number between and , but we cannot determine the exact value. The answer is (i). The correlation between x and y is the same as the correlation between y and x.

4 (b) Suppose we removed the point that is indicated by a * from the data represented in the plot. What would the correlation between length and width then be? (i) (ii) Larger than (iii) Smaller than (iv) Either larger or smaller than It is impossible to say which. The answer is (iii). The indicated point is (almost?) an outlier and makes the correlation larger than it otherwise be. When this point is removed, the correlation becomes smaller. E4. The correlation coefficient between two variables x and y is r What conclusion can we draw? (i) Because the correlation is so low, the relationship between x and y is not very strong, thus there is no use in studying this relationship. (ii) Because the correlation is so low, we only know that the linear relationship between x and y is not very strong, but there may a different relationship between the two variables. We need to first look at a scatterplot. (iii) The correlation between x and y is low, but that does not matter. We can still use least-squares regression to calculate an equation of the form yˆ ax b. (iv) None of the above. The answer is (ii). E5. Do heavier cars use more gasoline? To answer this question, a researcher randomly selected 15 cars. He collected data about the weight (in hundreds of pounds) and the mileage (mpg) for each car. From a scatterplot made with the data, a linear model seems appropriate: (a) Fill in the blank. The variable is the response variable in this study. mileage

5 (b) Fill in the blank. The variable is the explanatory variable in this study. weight (c) The percentage of variation in mileage that is accounted for by the linear relationship between mileage and weight is approximately 44%. What is the value of the correlation coefficient between the weight and the mileage of a car? Since r and r 0, therefore r E6. Which of the following scatterplots show (a) little or no association? (b) a negative association? (c) a linear association? (d) a moderately strong association? (e) a very strong association? (a) #1 shows little or no association. (b) #4 shows negative association. Increases in one variable are generally related to decreases in the other variable. (c) #2 and #4 each show a linear association. (d) #2, #3 and #4 show a moderately strong association. (e) None shows a very strong association.

6 E7. Below are several scatterplots. The calculated correlations are 0.736, , and Which is which? Write the correlations in appropriate plots. (a) (b) (c) (d) E8. Which of the following is true? a) correlation is a resistant measure of association b) correlation has no units c) correlation has a value between 0 and 1 d) the correlation coefficient and the slope of the regression line have opposite signs Correlation is not a resistant measure and it can be negative, if the slope of the line is negative. It also has the same sign as the slope. It has no units. Therefore, the answer is b).

7 F. Regression Example 1. Many high school students take either the SAT or the ACT. However, some students take both. Data were collected from 60 students who took both college entrance exams. The average SAT score was 912 with a standard deviation of 180. The average ACT score was 21 with a standard deviation of 5. The correlation between the two variables equals 0.817: (a) To predict the student s SAT score from a student s ACT score, what is the equation of the least-squares regression line? (i) yˆ x (ii) yˆ x (iii) yˆ x (iv) Cannot be determined from the information given. The explanatory variable (x) is the student s ACT score, while the response variable (y) is the student s SAT score. sy 180 b r ( 0.817) , s 5 x a y b x 912 (29.412) (21) The regression equation is The answer is (ii). 1 yˆ a bx x. (b) What fraction of the variation in the values of the SAT scores is accounted for by the linear relationship between SAT and ACT scores? (i) 66.7% (ii) 81.7% (iii) 90.4% (iv) Cannot be determined from the information given. 2 r (0.817) %. The answer is (i).

8 Example 2. Calculate the least-squared regression line of y on x from the following data: X Y i x i y i ( xi x) 2 ( y y) i Step 1. Find x and y x y i Step 2. Fill in the 4 th and 5 th columns x i y i ( xi x) 2 ( yi y) 2 xi x yi y xi x y s x s y s x i y s y

9 Sum Step 3. Find the standard deviations s x ( xi x) n s y 2 ( yi y) n Step 4. Complete the 6 th, 7 th and 8 th columns Step 5. Find r, a and b r 1 xi x y n 1 s x i y s y b r s y s x a y bx ( 45) a= yˆ a bx x **NOTE: Sometimes the textbook divides by "n" instead of "n-1" even though they are using a sample. This will change your numbers slightly. Practice Exam Questions

10 F1. Tell what each of the residual plots below indicates about the appropriateness of the linear model that was fit to the data. (a) The curved pattern in the residuals plot indicates that the linear model is not appropriate. The relationship is not linear. (b) The fanned pattern indicates heteroscedastic data. The models predicting power increases as the value of the explanatory variable increases. (c) The scattered residuals plot indicates an appropriate linear model. Remember the only graph of residual plots that represents a linear model, is one with NO patterns. It must be totally scattered. Therefore, the only one that is linear is c). F2. Recall that when we standardize the values of a variable, the standardized value has mean 0 and standard deviation 1. Suppose we measure two variables x and y on each of several subjects. We standardize both variables and compute the least-squares regression line of y on x for these standardized values. Suppose the slope of this least-squares regression line is What conclusion can we draw? (i) The intercept will be 1.0. (ii) The intercept will also be (iii) The correlation will be 1.0. (iv) The correlation will be s y 1 b1 r r r, so the correlation will be the same as the slope of the least-squares s x 1 regression line. The answer is (iv).

11 F3. In the National Hockey League a good predictor of the percentage of games won by a team is the number of goals the team allows during the season. Data were gathered for all 30 teams in the NHL and the scatterplot of their Winning Percentage against the number of Goals Allowed in the 2006/2007 Season with a fitted least-squares regression line is provided: The least-squares regression line and 2 r were calculated to be yˆ x, r where x is the is the number of goals allowed and y is the winning %. (a) Which of the following provides the best interpretation of the slope of the regression line? (i) If the Winning % increases by 1% then the number of Goals Allowed decreases by (ii) If a team were to allow 100 goals during the season their Winning % would be 90.95%. (iii) If Goals Allowed increases by one goal, the Winning % increases by 0.26%. (iv) If the Winning % increases by 1% then the number of Goals Allowed increases by (v) If Goals Allowed increases by one goal, the Winning % decreases by 0.26%. The answer is (v). The slope represents how much the response variable (Winning %) changes due to an increase in the explanatory variable (Goals Allowed) of one unit.

12 (b) Fill in the blank. The Montréal Canadiens team allowed 251 goals in 2006/2007. Using the least-squares regression line, the prediction of the team s Winning Percentage would be %. If x 251, then y ˆ (251) (c) For the Winning % and Goals Allowed least-squares regression analysis above, which of the following statements is (are) TRUE? (i) About 69% of the variation in the variable Goals Allowed can be explained by the least-squares regression of Winning % on Goals Allowed. (ii) About 69% of the variation in the variable Winning % can be explained by the least-squares regression of Winning % on Goals Allowed. (iii) If the correlation between Winning % and Goals Allowed were calculated it would be (iv) A and C are true. (v) B and C are true. The answer is (ii). F4. The least-squares regression line is fit to a set of data. One of the data points has a positive residual. Determine whether each of the following statements is true or false. (a) The correlation between the values of the response and explanatory variables must be positive. (b) The point must lie above the least-squares regression line. (c) The point must lie near the right edge of the scatterplot. (d) The point must be influential. (a) False (b) True (c) False (d) False

13 F5. The scatterplot for the set of 8 A&W menu items is provided below. The circled data point on the scatterplot is for the Grilled Chicken Sandwich. Which of the following statements about the circled data point on the scatterplot is/are TRUE? (i) This point would likely be considered an outlier. (ii) The residual associated with this data point will have a negative value. (iii) This point may be considered influential but that depends on how much it affects the plot of the residuals. (iv) Only A and B are true. (v) A, B, and C are true. The point is clearly far from the regression line, so it is an outlier. The point also lies below the regression line, so its residual is negative. The answer is (iv).

14 F6. Four different residual plots are shown below. Which plots indicate that the linear model is not appropriate? (A) (B) (C) (D) A residual plot show show no pattern, no direction and no shape in order to represent a linear model. Therefore, a) and d) can not represent linear models. F7. Recall the following question from section E. in your booklet: Do heavier cars use more gasoline? To answer this question, a researcher randomly selected 15 cars. He collected data about the weight (in hundreds of pounds) and the mileage (mpg) for each car. From a scatterplot made with the data, a linear model seems appropriate: (a) The equation of the least-squares regression line is yˆ x. Which of the following descriptions of the value of the slope is the correct description? (i) The mileage is expected to decrease by when the weight of a car increases by 1 pound. (ii) The mileage is expected to decrease by when the weight of a car increases by 100 pounds. (iii) The mileage is expected to decrease by when the weight of a car increases by 100 pounds.

15 (iv) We cannot interpret the slope because we cannot have a negative weight of a car. The answer is (ii). The slope represents how much the response variable (mileage) changes due to an increase in the explanatory variable (weight) of one unit (hundreds of pounds). (b) The percentage of variation in mileage that is accounted for by the linear relationship between mileage and weight is approximately 44%. What is the value of the correlation coefficient between the weight and the mileage of a car? Since r and r 0, therefore r F8. A study compared the effectiveness of several antidepressants by examining the experiments in which they had passed the FDA requirements. Each of those experiments com-pared the active drug with a placebo, an inert pill given to some of the subjects. In each experiment some patients treated with the placebo had improved, a phenomenon called the placebo effect. Patients depression levels were evaluated on the Hamilton Depression Rating Scale, where larger numbers indicate greater improvement. The scatterplot of mean improvement levels for the antidepressants vs. placebos for several experiments is shown below. (a) Is it appropriate to calculate the correlation? Explain. It is appropriate to calculate correlation. Both placebo improvement and treated improvement are quantitative variables, the scatterplot shows an association that is straight enough, and there are no outliers. (b) The correlation is Explain what we have learned about the results of these experiments.

16 There is a strong, positive, straight association between placebo and treated improvement. Experiments that showed a greater placebo effect also showed a greater mean improvement among patients who took an antidepressant. F9. The correlation between Fuel Efficiency ( as measured by miles per gallon) and Price of 150 cars at a large dealership is r Explain whether or not each of these possible conclusions is justified. (a) The more you pay, the lower the fuel efficiency of your car will be. No. We don t know this from correlation alone. The relationship between fuel efficiency and price may be non-linear, or the relationship may contain outliers. (b) The form of the relationship between Fuel Efficiency and Price is moderately straight. No. We can t tell the form of the relationship between fuel efficiency and price. We need to look at the scatterplot. (c) There are several outliers that explain the low correlation. No. The correlation between fuel efficiency and price doesn t tell us anything about outliers. (d) If we measure Fuel Efficiency in kilometers per liter in-stead of miles per gallon, the correlation will increase. No. Correlation is based on z-scores, and is unaffected by changes in units.

17 F10. An experiment examined the relationship between the fuel economy (mpg) and horsepower for 15 models of cars. Further analysis produces the regression model mpg HP. (a) If the car you are thinking of buying has a 200- horsepower engine, what does this model suggest your gas mileage would be?. mpg HP (200) mpg. (b) Explain what the slope means in the context. According to the model, slope means that as horsepower increases by 1 HP, we expect mpg to go down by F11. Fill in the missing information in the table below. Show your work. x s x y s y r yˆ a bx (a) (b) (c) yˆ 10 15x (d) yˆ 30 2x x s y s x y r yˆ a bx (a) yˆ x (b) yˆ x (c) yˆ 10 15x (d) yˆ 30 2x s y 6 (a) b r ( 0.2) 0. 3, a y bx 18 ( 0.3) (30) 27, s 4 x yˆ a bx x. s y 10 (b) b r ( 0.9) 0. 5, a y bx 60 (0.5) (100) 10, s 18 x

18 yˆ a bx x. (c) y a bx x x 4, s b r s y x r r (d) y a bx x x 6, s y 4 4 b r 2 ( 0.6) s x ( 0.6) 1.2. s s 2 x x F12. Refer to the regression analysis for average attendance and games won by American League baseball teams, shown below: Dependent variable is: Home Attendance R-squared = 48.5% Variable Coefficient Constant Wins (a) Write the equation of the regression line. Attenˆdance (Wins) (b) Estimate the Average Attendance for a team with 50 Wins.

19 Attenˆdance (50) 12,851. (Note: This is an extrapolation.) (c) Interpret the meaning of the slope of the regression line in this context. For each additional win, the model predicts an increase in attendance of people on average. (d) In general, what would a negative residual mean in this context? A negative residual means that the team s actual attendance is lower than the attendance model predicts for a team with as many wins. (e) The St. Louis Cardinals, the 2006 World Champions, are not included in these data because they are a National League team. During the 2006 regular season, the Cardinals won 83 games and averaged 42,588 fans at their home games. Calculate the residual for this team, and explain what it means. Attenˆdance (83) 30, Residual observed - predicted 42,588 30, , The large positive residual shows that home attendance for the St. Louis Cardinals was much higher than is predicted according to the regression line for American League attendance.

20 F13. Each of the following two scatterplots shows a cluster of points and one stray point. For each, answer these questions: (i) Do you think that point is an influential point? (ii) If that point were removed from the data, would the correlation become stronger or weaker? Explain. (iii If that point were removed from the data, would the slope of the regression line increase or decrease? Explain. (a) (i) The point is influential. It is well away from the mean of the explanatory variable, and has enough leverage to change the slope of the regression line. (ii) If the point were removed, the correlation would become stronger. Without the point, the positive association would be reinforced. (iii) The slope would increase, becoming steeper after the removal of the point. The regression line would follow the general cloud of points more closely. (b) (i) The point is influential. The point alone gives the scatterplot the appearance of an overall positive direction, when the points are actually fairly scattered. (ii) If the point were removed, the correlation would become weaker. Without the point, there would be very little evidence of linear association. (iii) The slope would decrease, from a positive slope to a slope near 0. Without the point, the slope of the regression line would be nearly flat. F14. A stop drinking pamphlet says Children of mothers who drink during pregnancy scored ten points lower on intelligence tests at age 4 than children of mothers who never drank during pregnancy. List some lurking variables that could explain the association between drinking during pregnancy and children s test scores. Answers will vary. Some examples include: whether or not mothers took vitamins and ate healthy during pregnancy, nutrition of child during first four years, whether or not illegal drugs were consumed, stimulation during the first four years, smoking during pregnancy, etc.

21 F15. Mean height of Canadian women in 20's is about 64 inches and the standard deviation is about 2.7 inches. The mean height of men the same age is about 69.3 inches with a standard deviation of about 2.8 inches. Suppose that the correlation between the heights of husbands and wives is about r=0.6. a) Find the slope and intercept of the regression line. Let X=women and Y= men Then, we are given: r=0.6 Slope= b= Intercept a= b) Find the equation of the least-squares regression G. Two-Way Tables Practice Exam Questions G1. The following two-way table shows the age and sex of all undergraduate university students at a particular university. Age Group Female Male Total years

22 Total a) How many university undergraduates are there at this university?13950 b) Find the marginal distribution of age group years= % years= % etc. c) Find the conditional distribution of females age % 6500 G2. Given the following two-way table, answer the questions below. University students were asked how likely they think it will be that they earn a 6-digit salary in the next 20 years. Opinion Female Male Total Almost no chance Some chance, but not likely

23 A chance A good chance Almost certain Total a) How many individuals are described using this table? 3450 b) How many males are among those surveyed? 1750 c) Find the percent of females among the respondents % 3450 d) Does part c) represent a marginal or conditional distribution? Why? It represents the marginal distribution of sex. e) What percent of females thought they had a good chance to earn 6-figures in the next twenty years? % 1700 f) Does part e) represent a marginal or conditional distribution? Why? The conditional distribution of chance to earn 6-figures among females. G3. The following two-way table describes the age and sex of university students at a particular university.

24 Age Group Female Male Total Total a) How many university students are there? b) Find the marginal distribution of each age group years= % years= % years= % 35+ years= %

25 G4. Given the following table, find each of the following: Male Female Total Blue Brown Green/Other Total a) How many individuals are described by this table? 80 b) How many females were among the respondents? 37 c) The percent of males among the respondents was %. 54% d) Your answer in c) represents what type of distribution? The marginal distribution of sex. e) What percent of females have brown eyes? % f) Your answer in e) represents what type of distribution? The conditional distribution of brown eyes among females. g) What percent of people with green eyes were male? % 15 h) Your answer in g) represents what type of distribution? The conditional distribution of males among people with green eyes.

26 G5. Show that the following data is an example of Simpson's Paradox. Department Men Women Applicants Admitted Applicants Admitted A % % B % 25 68% C % % D % % E % % F 272 6% 341 7% This is a real-life example from data of the University of California, Berkeley. They were sued for bias against women who had applied for admission to graduate schools there. If you look at the total data for applicants admitted, you get the table below: Applicants Admitted Men % Women % When you look at the chart above and examine individual departments, however, there is no significant bias against women. It appears sometimes the women applied in cases where very few applicants would be admitted. This is an example of Simpson's Paradox. G6. Given the following table of some respondents favourite leisure activities, find each of the following: Male Female Total Dance Sport TV Total a) How many individuals are described by this table? 50 b) How many females were among the respondents? 30

27 c) The percent of males among the respondents was % % d) Your answer in d) represents what type of distribution? The marginal distribution of sex. e) What percent of females have dance as their favourite leisure activity? % 30 f) Your answer in e) represents what type of distribution? The conditional distribution of leisure activity among females. g) What percent of people who prefer sports as their favourite leisure activity are male? % 16 h) Your answer in g) represents what type of distribution? The conditional distribution of males among favourite leisure activities. G7. Given the following two-way table about transportation to work for a given company, answers the questions below: Job Class Car Bus Train Total Management Labour Total a) How many employees are there in this company? 420 b) What percentage of employees are in management? %

28 c) What type of distribution does your answer to part b) represent? The marginal distribution of employees. d) What percentage of employees take a car? % 420 e) What type of distribution does your answer to part d) represent? The marginal distribution of mode of transportation. f) What percentage of management take a train? % 90 g) What type of distribution does your answer to f) represent? The conditional distribution of taking a train among management. H. Methods of Sampling

29 Practice Exam Questions H1. To survey Western undergrads use of additional spam filters to eliminate spam , 200 undergrads were chosen at random and ed a link to the survey. However, 50 of the 200 students had spam filters that blocked the message, so these students didn t receive the link and so didn t respond to the survey. Of the 150 respondents, 30 were using additional spam filters. In writing up the report, the surveyor stated that 20% of the students reported using additional spam filters. (a) What is the surveyor s parameter of interest? The percentage of Western undergrads who use additional spam filters. (b) What is the surveyor s estimate of the parameter? 20% (c) True or False? The estimate is probably too low. TRUE. (d) True or False? This is an example of a convenience sample. FALSE.

30 H2. In a cross-canada phone survey to determine the popularity of CBC radio, phone surveyors contacted 100 randomly selected households in each province. The phone surveyors found that 10% of the chosen households had had CBC radio on in the house at some time during that week. (a) What type of probability sampling did the surveyors use? Stratified sample. (b) The variable of interest in the survey is: (pick the best answer) (i) the percentage of all households in Canada that had CBC radio on sometime during that week. (ii) 10%. (iii) the number of households contacted. (iv) CBC radio status (whether or not it was listened to that week). (iv) CBC radio status. H3. In a study of the effects of Vitamin C on cold prevention, a researcher chose 50 participants at random. He then made up 50 identical pill bottles. In half, the researcher placed Vitamin C tablets. In the other half, the researcher put identical looking and tasting sugar pills. The researcher then gave out the bottles at random to the 50 participants, not telling them which type of pill they received, but noting the type in his data file. Each participant took the pills daily for the next six months, and also recorded the number of colds incurred in the 6-month period. (a) True of False? This is a blind study. TRUE. (b) True of False? This is a double blind study. FALSE.

31 (c) True of False? This experiment involves a placebo. TRUE. H4. Two variables in a study are said to be confounded if (choose one): (i) we cannot separate their effects on a response variable. (ii) they are highly correlated. (iii) one of them is a placebo. (iv) both of them have values that are outliers. (i) we cannot separate their effects on a response variable. H5. An opinion poll is given to the members of a local gym. The members are first split into two groups by gender, and then a simple random sample of 50 members is chosen from each group and issued the questionnaire. This is an example of (i) a stratified sample. (ii) a block design. (iii) a multi-stage sample. (iv) a convenience sample. (v) double blinding. (i) a stratified sample. H6. Radon is a radioactive gas sometimes found in homes. A health inspector wants to determine the levels of radon in a particular town s houses. He partitions a map of the town into a grid of 100 neighbourhoods: 50 neighbourhoods on the west side (the poorer section of the town), and 50 neighbourhoods on the east side (the wealthier section). He randomly chooses 10 of the west side neighbourhoods and randomly chooses 10 of the east side neighbourhoods. Within each of the chosen neighbourhoods, he randomly chooses three houses. He measures the radon in each of the chosen houses. What type of design is this? (Choose one) (i) a matched pairs design. (ii) a two-factor design. (iii) a multi-stage design. (iv) a stratified design.

32 (v) a simple random sample. (iii) a multi-stage design. H7. Indicate which of the following is/are true for clinical trials which are double-blind, by circling the corresponding letter(s). (i) The placebo effect is eliminated. (ii) Neither subject nor medical staff knows which treatment is applied. (iii) They are most appropriate for matched pairs designs. (iv) The data will be analyzed without regard to which treatments were applied. (v) The results are encoded to blind information about the subjects. (ii) Neither subject nor medical staff knows which treatment is applied. H8. Violent acts on prime-time TV. A typical hour of prime-time television shows three to five violent acts. Linking family interviews and police records shows a clear association between time spent watching TV as a child and later aggressive behaviour. a) Explain why this is an observational study rather than an experiment. What are the explanatory and response variables? Answer: It is an observational study because we are not assigning treatments (ie. controlling the number of hours a child watches TV). b) Suggest several lurking variables describing a child s home life that may be related to how much TV he or she watches. Explain why this makes it difficult to conclude that more TV causes more aggressive behaviour. Answer: Other lurking variables could be: -hours parents work -neighourhood where child lives -etc There might be another variable that is causing the aggressive behaviour. That variable is called a lurking variable.

33 H9. What is the preferred treatment for breast cancer that is detected in its early stages? The most common treatment was once mastectomy (removal of the breast). It is now usual to remove the tumor and nearby lymph nodes, followed by radiation. To study whether these treatments differ in their effectiveness, a medical team examines the records of 25 large hospitals and compares the survival times after surgery of all women who have had either treatment. a) What are the explanatory and response variables? Ans: Which surgery was performed is the explanatory variable; survival time is the response. b) Explain carefully why this study is or is not an experiment Ans. It is not an experiment because the study does not impose treatments on the subjects. It is purely observational c) Do you think this study will show whether a mastectomy causes longer average survival time? Explain your answer carefully [your explanation is intended for readers of the Toronto Sun daily newspaper (not a highbrow paper)]. Ans. No. Since patients were not randomly assigned to treatments, differences in results may be due to confounded factors. E.g., doctors may recommend treatment based on the patient s condition - perhaps some doctors tend to suggest one treatment for more advanced cases; those patients would have a poorer prognosis than the patients for whom the doctors suggest the other treatment. H10. Suppose that we want to select a sample of students from your STAT 1024 lecture class (150 students in total). [ random below means by using the Random Number table the customary way] i) If we assign each student in the classroom a RN from 001 to 150, and then use a RN table to pick two distinct random numbers from , and then take the corresponding students, what do we call this particular type of random sample? SRS ii) If we select randomly five students from the centre section, and then three at random from the section on the left side, and finally three randomly from the section on the right, what type of sampling design is this? Stratified sampling

34 iii) Suppose that we order the students in attendance in some clear simple fashion (say left seat to right seat, bottom row to top row in left section, then left to right, bottom to top in centre, then left to right, bottom to top in right section), and then select every 8 th student, after drawing an appropriate random number. What do we call this type of sampling design? Systematic sampling. iv) If we randomly select 6 rows in the classroom, then 2 students randomly from each selected row, what do we call this type of sampling design? Multistage (cluster) sampling v) Suppose that the prof of a particular lecture section wants to learn something about the opinions of students registered in his lecture section. At the end of class, one Friday, he draws a sample (proceeding as in scheme (i) above) of 10 students from the class and reads to them the three statements below. Each student is asked to pull out and submit a piece of paper, writing on it only one thing the statement that he/she agrees the most with. Statistics is more interesting than I had anticipated before starting this course Statistics is less interesting than I had anticipated before starting this course Statistics is about as (un)interesting as I had anticipated before starting this course Describe below the two most glaring sources of bias in this survey: (i) undercoverage (not all enrolled will be in attendance) (ii) interviewer bias (they might want to please the prof) H11. An opinion poll contacts 1200 Canadian adults and asks them "Which political party do you think has better ideas for leading our country?" In all, 700 say "liberal". In this setting, the sample is: a) All Canadians b) the 1200 Canadians surveyed c) the 700 people who chose liberal Solution

35 The answer is b). H12. See Question H11. Which is the population? a) All Canadians b) the 1200 Canadians surveyed c) the 700 people who chose liberal Solution The answer is a). H13. You must choose a SRS of 10 of the 400 stores that sell food in a particular city. How would you label this population in order to obtain a SRS? a) 1,2,3,...,440 b) 001,002,...,400 c) 000,001,002,...,400 The answer is b). All numbers must be the same number of digits and there must be 400 of them. H14. Choose a SRS of 3 people from the following students: Anderson 00 Brook 01 Cole 02 Denning 03 Edwards 04 Frank 05 Goring 06 Harrison 07 Kim 08 Manning 09 Use line 130 from Table B.

36 Go through the numbers from left to right and look at two-digit numbers and circle any that are in the set "01, 02,...10". The numbers you get are 05, 00, 04. So, we choose Frank, Anderson and Edwards H15. Using line 101 of random digits from Table B, select a SRS of 5 students of a class of 15. Label the students 01 to 15 in alphabetical order. Which students will your SRS contain? Line 101 is: When you circle the two-digit numbers that are in the list, you eventually (after three lines of the table!) get: 05, 13, 09, 07, 02 So, we would select whichever students represented these numbers alphabetically.