1.	A polling company working for a candidate for governor surveys a sample of 2500 registered voters in the state to determine if they are in agreement with the candidate's stand on gun control.  Describe the population for this study. 	

2.	A biologist draws a sample of 200 fish from a lake to test for mercury levels.  She finds that 8% have levels above limits set as healthy.  Describe the population for this study. 	

3.	In order to determine if students on a college campus are in favor of a tuition hike to pay for expanded parking services, a member of the student senate surveys 25 people in a commuter parking lot.  Why is this a poor sampling technique? 	

4.	Convenience samples are said to be highly likely to produce bias in survey results.  Explain why this is true. 	

5.	Explain the difference between bias and variability in sampling results. 	

6.	We wish to know what proportion of students at a major university believe too much emphasis is placed on athletics at the school.  Explain how we could choose a sample of 500 students to reduce the possibility of bias in the results. 	

7.	In order to determine what proportion of a town's residents approve of a new plan for trash collection, the town council placed an ad in the newspaper asking residents to phone in their opinions.  Explain why the results of this poll may differ from the actual beliefs of all residents in the town. 	

8.	Define a simple random sample. 	

9.	Can we eliminate variability in results of sampling?  Why or why not? 	

10.	101	
01033	
08705	
42934	
79257	
89138	
21506	
26797	

102	
49105	
00755	
39242	
50772	
44036	
54518	
56865	

103	
61589	
35486	
59500	
20060	
89769	
54870	
75586	

104	
08900	
87788	
73717	
19287	
69954	
45917	
80026	

105	
75029	
51052	
25648	
02523	
84300	
83093	
39852	

106	
91276	
88988	
12439	
73741	
30492	
19280	
41255	

107	
74008	
72750	
70742	
67769	
72837	
27098	
07049	

108	
98406	
27011	
76385	
15212	
03806	
85928	
76385	

Use the random digits table, beginning at line 103, to choose a sample of four people from the following list:
 
01 Adams	
06 Ford	
11 Kramer	
16 Post	

02 Brown	
07 Goodman	
12 Loomis	
17 Quayle	

03 Cook	
08 Harris	
13 Martin	
18 Rogers	

04 Davis	
09 Inez	
14 Norton	
19 Stevens	

05 Elliot	
10 Jones	
15 O'Hare	
20 Thompson	

11.	We must use a random digits table to choose a sample of eight names from the roster of a club with 100 members.  Why can we use two-digit numbers from the table to select our sample? 	

12.	The marketing department of a large national corporation wishes to determine what proportion of the residents of a state may be interested in buying its new product.  Describe how the corporation might use a multi-stage random sampling process to choose a sample of the state's residents to survey. 	

13.	A high school principal wishes to determine what proportion of the school's students like the new school mascot.  The principal decides to survey every 25th name from the school enrollment records (an alphabetical list of all students at the school).  Is this a valid simple random sampling technique?  Why or why not? 	

14.	In a poll of 2500 residents of a state it is found that 480 are in favor of naming the grasshopper the state insect.  What is the sample proportion for this poll?	

15.	A marketing department surveys 1500 shoppers and finds that 950 would visit a new store more often if were open Sunday evenings.  What is the sample proportion in this survey?	

16.	Why do opinion polls usually report a "margin of error" with the results of a survey?  What does the margin of error mean? 	

17.	What is the difference between an observational study and an experiment? 	

18.	One July, the city council of a small town decides to impose an experimental curfew on all residents under 18 to cut down on loitering in the town square.  After four months, the number of teens found in the square after dark has decreased 80%, and the council declares the curfew a success.  Explain why this conclusion may not be valid. 	

19.	A farmer believes that exposing chickens to classical music will cause them to produce more eggs.  Describe how the farmer may design a randomized comparative experiment to test this theory. 	

20.	A school superintendent believes a new approach to teaching children to read will produce better standardized test scores in the district.  Describe how the superintendent may design a randomized comparative experiment to test this theory. 	

21.	A school principal is concerned with the increasing level of absenteeism in the school.  A meeting of parents, teachers, and students is called at which the principal expresses her concern and describes an experimental program that will be instituted to try to curb absenteeism.  After two months, absenteeism is down by 15%.  Explain how confounding variables may have affected the results of the experiment. 	

22.	Medical experiments are frequently double blind.  Explain what this means and why medical experiments are designed this way. 	

23.	Describe what is meant by the placebo effect in an experiment. 	

24.	How does a randomized comparative experiment control the effects of confounding variables? 	

25.	What does it mean to say that the results of an experiment are statistically significant? 	

26.	Officials at a university want to determine the percentage of students who favor the allocation of a percentage of tuition funds toward the construction of a new campus parking garage. To find this out, a survey is conducted. One thousand people driving through the administration building parking lot are surveyed, and it is found that 75% of these people favor the garage. Explain why this conclusion might not be valid. 	

27.	Officials at a university want to determine the percentage of students who favor the allocation of a percentage of tuition funds toward the construction of a new campus parking garage. To find this out, a survey is conducted. One thousand people driving through the administration building parking lot are surveyed, and it is found that 75% of these people favor the garage. What is the population in this study? What is the sample? 	

28.	A new stadium is being planned for the local professional football team. One of the proposed funding methods involves the allocation of tax monies to build the stadium. To determine the public opinion of this plan, the first 100 people entering the stadium for a game are surveyed. Explain why the results of this survey might not be valid. 	

29.	A recent survey of 536 employees of U.S. corporations determined that 84% of them feel that the executives who run their companies are ethical. Determine the 95% confidence interval for this survey. 	

30.	A survey of 127 patients in a particular hospital determined that 54% of them felt that they were receiving excellent care. Determine the 95% confidence interval for this survey. 	

Answer Key

1.	The population is all registered voters in the state.	
2.	The population is all fish in the lake.	
3.	The students who are being surveyed are commuters who drive to campus and are likely to have different views on parking services than the general student body.  This sampling technique would leave out the opinions of students living on campus or others without cars.	
4.	Convenience samples are drawn from individuals who are the most easily available; and therefore they are unlikely to draw from all of the target population for a survey.	
5.	Variability refers to the natural differences in results that occur from one random sample of a population to the next.  Variability in sampling results cannot be avoided, but the overall pattern of variability can be described.  Bias in sampling results refers to a systematic error caused by poor sampling technique or a poorly worded survey.	
6.	Obtain a list of currently enrolled students from the university registrar.  Number the list of students and then use a table of random digits to select 500 numbers corresponding to students on the enrollment list and contact these students.	
7.	The sampling technique described uses self-selection.  Only those residents with extreme views on the new plan are likely to respond to the advertisement.  A second problem with the poll technique described is that not all residents who will be affected by the new trash collection plan are likely to read the newspaper.  The opinions of a large number of residents are therefore unlikely to be included in the results of the poll.	
8.	A simple random sample is one in which every group from the population has an equally likely chance of being chosen.	
9.	We cannot eliminate variability in the results of sampling.  Variability refers to the natural differences that occur from one sample to the next in a population.	
10.	Those chosen would be: 02 Brown, 10 Jones, 17 Quayle, and 19 Stevens.	
11.	We can number the names on the roster using the labels 00, 01, 02, 03, . . . 96, 97, 98, 99. This list includes 100 distinct labels.  (Using this list instead of 001, 002, . . . 098, 099, 100 would result in a more efficient use of the random digits table.  Every two-digit portion read from the table would refer to a name on the roster where only 1/10 of the three-digit portions would be useable.)	
12.	Answers may vary.  First, the Marketing Department would break the state up into many contiguous areas, possibly using county borders.  They would randomly select several of these counties.  Each county selected would be broken up into smaller regions, perhaps neighborhoods.  Several neighborhoods in each selected county would be randomly chosen.  Within each chosen neighborhood, several individual families would be randomly chosen to be surveyed.	
13.	Taking every 25th name from an alphabetical listing of students is not a valid simple random sampling technique because no two students who follow one another on the list could ever be part of the sample.  This contradicts the idea that in a simple random sample, every collection of individuals has an equal chance of being chosen.	
14.	480/2500 = 19.2%
The sample proportion of residents in favor of naming the grasshopper state insect is 19.2%.	
15.	950/1500 = 63.3%
The sample proportion of the survey of shoppers who would visit a store more frequently if it were open Sunday evenings is 63.3%.	
16.	The results of an opinion poll are unlikely to match exactly the views of the whole population.  Instead, those reporting poll results can be confident that the actual population results fall in an interval around the poll results.  The margin of error defines the size of this interval.	
17.	An observational study observes individuals and measures some variable of interest, but does not try to change the behavior or conditions of the subjects.  In an experiment, the researcher imposes some treatment or condition on some of the individuals in the study and then observes their response.	
18.	Answers may vary.  In the four months since the curfew began, school would also have started.  It is possible that teens are now home doing homework after dark and would have been even without the curfew.  It is also possible that the cooler temperatures associated with fall months led to a decline in teens in the square after dark.	
19.	Answers may vary.  The farmer randomly divides his chickens into two groups.  Keeping all other conditions (housing, food, etc.) the same, he plays classical music to one randomly chosen group.  The other group of chickens will be in a coop without music.  After two months, the egg production of the two groups of chickens will be compared.	
20.	Answers may vary.  Children in the district will be divided randomly into two groups.  This random division will, hopefully, minimize differences between the groups on IQ, parental education level, or other factors the superintendent believes may have an impact on children's test scores.  One group is chosen to receive the new approach to reading instruction.  The other group is taught reading using traditional methods.  (It would be best if the same teacher taught both groups, changing only the instruction method.)  The standardized test scores of the two groups are compared at the end of the year.	
21.	The meeting of parents, teachers, and students may have brought to the attention of parents problems associated with absenteeism in the school.  Parents may have reacted with measures to increase their children's attendance in ways unrelated to the experimental program.	
22.	In a double blind experiment, neither the participant nor the person collecting the data knows who is taking the experimental treatment and who is taking the placebo.  This is done so that when participants report on their health they are not swayed in their own assessments by the thought of being on an experimental treatment.  Also, recorders will not unconsciously exaggerate participants conditions because they do not know which treatment participants are receiving.  Running a study as double blind helps to combat the placebo effect.	
23.	The placebo effect refers to the effects of a dummy treatment on the subjects of a study.  People who believe they are receiving an experimental treatment designed to make them perform better may actually have a better performance due to the power of suggestion, regardless of the actual effectiveness of the treatment.	
24.	In a randomized comparative experiment, subjects are randomly divided into two groups, one of which receives the experimental treatment and the other the traditional treatment.  Since the two groups are chosen at random, any possible confounding variables should act equally on both groups.  This allows differences in outcomes to more confidently be attributed to the treatment.	
25.	The results of an experiment are called "statistically significant" if they are greater than one would expect to occur by chance from a group drawn at random from the population of the study.	
26.	Answers may vary. The population of this survey would be all students at the university, and not all of them are likely to be driving through the administration building parking lot, so the population is not well represented. In fact, the sample was taken at a location that is unlikely to include any students at all; generally, people parking at an administration building are likely to be faculty, staff, administrators or university guests. Also, people who are driving are more likely to favor a parking garage than people who do not drive to campus, so the students who use other modes of transportation would not be represented by this survey even if students did use that parking lot.	
27.	The population is all students at this particular university. The sample is the 1000 people actually surveyed.	
28.	Answers may vary. People attending the game are likely to be football fans, and in particular, the first 100 people to arrive are likely to be very eager fans. Fans of the game would be more favorable toward the construction of a new stadium and possibly would not mind this allocation of tax monies, whereas people who do not attend the games at all might oppose this funding method.  People who do not attend the games would not be represented in this sample.	
29.	Approximately, the interval between 80.8% and 87.2%.	
30.	Approximately, the interval between 45.2% and 62.8%.