CH 4

a simple random sample of size n is defined to be

a sample of size n chosen in such a way that every sample of size n in the population has an equal chance to be selected

sample survey

a study that collects data from a sample that is chosen to represent a specific population

surverys

the researcher asks individuals to answer questions about their opinions or practices, association between what causes what is gained

a poll conducted by the student newspaper asked, "who do you believe will win the Ohio State undergrad student government elections?" in order to vote, one had to access the student newspaper's web site and record ones vote. the results of the poll were summarized in a pie graph similar to the graph below. which of the following statements is true about these results?

the results of the survey are unreliable because response to the survey was voluntary

the principle reason for the use of replication in designing experiments is that it

utilizes enough experimental units so that any differences in the effects of treatments can be distinguished from chance variation among the groups

does caffeine improve exam performance? suppose half of the students from the 8:30 section of a course are randomly allocated to the treatment group (two cups of coffee) and the other half to the control group (two cups of decaf). in addition, half of the 9:30 students are randomly allocated to the treatment group, the other half to the control group. this is an example of a

block design

agricultural scientists for a chemical company wants to determine if a newly developed fertilizer produces heavier tomatoes than the fertilizer they currently manufacture. for their first pilot study, they have 24 healthy young tomato plants growing in individual pots. give a written description of a completely randomized, controlled experiment to test whether the new fertilizer produces heavier tomatoes

IN SHORT: random assignment, control environment, comparison

blocks

a group of experimental units or subjects that have some common characteristic that could possibly affect the response to the treatment. blocks are another form of control since they tend to control the effects of possible confounding variables by bringing those variables into the experiment to form the blocks thus reducing or possible eliminating the possible confounding variable's effect on variability between the treatment and control groups

which of these statements about a table of random digits is true? A. every row must have exactly the same number of 0's and 1's B. in the entire table, there are exactly the same number of 0's and 1's C. If you look at 100 consecutive pairs of digits anywhere in the table, exactly 1 pair is 00 D. All of these E. none of these

none of these is true

in order to assess the effects of exercise on reducing cholesterol, a researcher took a random sample of fifty people from a local gym who exercised regularly an another random sample of fifty people from the surrounding community who did not exercise regularly. they all reported to a clinic to have their cholesterol measured. the subjects were unaware of the purpose of the study, and the technician measuring the cholesterol was not aware of whether or not subjects exercised regularly. this is an

observational study

control group

one of the groups when designing an experiment, typically receives a dummy treatment or no treatment at all

a college admission officer wants to know what the most important factors are that high school seniors consider when they choose where to apply to college. she conducts a telephone survey by taking a simple random sample of applicants to her college. identify the population and the sample

population: high school seniors apply to college sample: randomly selected applicants from her college that responded

anecdote

the researcher simply recounts instances known to him or her. has no real value because no real evidence is taken, it is just a memory

strata vs cluster

we want each stratum to contain similar individuals and for large differences to exist between strata. for a cluster sample, we'd like each cluster to look just like the population, but on a smaller scale. unfortunately, cluster samples don't offer the statistical advantage of better information about the population that stratified random samples do

what do experiments establish?

a cause and effect relationship between variables and control the effects due to other variables

statistically significant

an observed effect so large that it would rarely occur by chance, we can then hopefully establish a casual relationship

which of the following isnt a principle of experimental design? control replication blocking randomization all of these

blocking

census

collects data from every individual in the population

what are the four principles of experimental design?

control, randomization, replication, comparison

the principle reason for the use of controls in designing experiments is that it

ensures that the only consistent differences between groups are the treatments administered by keeping other variables constant during the experiment

comparison

experiments must compare two or more treatments to avoid confounding

agricultural scientists for a chemical company wants to determine if a newly developed fertilizer produces heavier tomatoes than the fertilizer they currently manufacture. for their first pilot study, they have 24 healthy young tomato plants growing in individual pots. use the section from the random digit table to explain how to carry out the randomization required by your design

label the plants using 2 digit numbers from 01 - 24. starting from the left to right, read off the first 12 2 digit unique numbers from 01 - 24. ignore only repeating numbers not from 01 - 24. assign the first 12 corresponding plants to the fertilizer they currently manufacture. assign the remaining 12 plants to the fertilizer they currently manufacture. then compare the effectiveness that the fertilizers had on the tomatoes heaviness

you plan to give a math achievement test to samples of 15 year old's from both the US and Korea in order to compare mathematics knowledge in the two countries. in each country you will randomly choose 300 students from low income families, 400 students from middle income families, 200 students from high income family. the sample of Korea is a

stratified random sample

a sportswriter wants to know how strongly Lafayette residents support the local minor league baseball team, the Lafayette Leopards. he stands outside the stadium before a game and interviews the first 20 people who enter the stadium. what is the sample for this survey?

the 20 people who the sportswriter their opinion

you decide to conduct a survey about the quality of food served in the school cafeteria by selecting the first 25 female students as they enter the cafeteria for lunch on a specific day next week. describe a source of bias that may result from using this method and how that bias may impact your result

under coverage bias may occur because you are not representing the population as a whole from convenience sampling. those who get there earliest may have better opinions of food, overestimating its quality

just before the presidential election of 1936, a magazine incorrectly predicted that Alf Landon would defeat Roosevelt. Landon lost in a landslide. it turned out that the magazine only polled its own subscribers, plus others from a list of automobile owners and a list of people who had telephone service. all three groups had a higher typical income during the great depression. this is an example of

undercoverage

a local tax reform group polls the residents of the school district of the school district and asks the question, "do you think the school board should stop spending taxpayers money on non essential arts programs in elementary schools? the results of this poll are likely to

underestimate the support for arts programs because of non coverage

confounding

when the effect of other variables on the response variable cannot be distinguished from each other

study

a process of gathering data and drawing conclusion from that data EX of studies: anecdote, surveys, observational studies, and experiments

a sportswriter wants to know how strongly Lafayette residents support the local minor league baseball team, the Lafayette Leopards. he stands outside the stadium before a game and interviews the first 20 people who enter the stadium. what is the intended population for this survey?

all residents of Lafayette

why should experiments include a control group?

allows a group to compare other groups to so if one decreases and one doesn't you could reasonably conclude its due to the other treatments

blocking

an experimental design where the researcher first separates the sample into blocks based on common characteristics and only then randomly assign subjects within each block to the treatment groups of control group

confounding variables are

any variables whose effect on the response variable cannot be separated from each other

your school will send a delegation of 35 seniors to a student life convention. 200 girls and 150 boys are eligible to be chosen. a sample of 20 girls and a separate sample of 15 boys are each selected randomly to attend the convention. beginning at line 108 in the random digit table, select the first three senior girls to be in the sample. explain your procedure clearly.

assign the girls 3 digit numbers 001-200. Read off from left to right the first 3 three digit numbers, ignoring any numbers not in the range 001-200 and any repeated numbers, to result in three randomly selected unique numbers

we wish to choose a simple random sample of size three from the following employees of a small company. to do this, we will use the numerical labels attatched to the names below. 1. Bechhofer 2. Brown 3.Ito 4. Kesten 5. Kiefer 6. Spitzer 7. Taylor 8.Wald 9. Weiss. we will also use the following list of random digits, reading the list from left to right, starting at the beginning of the list 11793 20495 05907 11384 44982 20751 27498 the simple random sample is

bechhofer, taylor, weiss

the 24 hour customer service call center for a major electronics manufacturer is trying to determine how to keep customers who are on hold as happy as possible. they want to examine whether the type of music they play while customers are on hold and whether or not there is a periodically repeated recorded message have an impact on customer satisfaction. they plan to randomly select customers who are on hold and play one of three different types of music (smooth jazz, classical, or show tunes) and either play the recorded message or not. after the entire call is over, they will ask the customers to rate their overall customer service experience. suppose the company is concerned that the time when the call is made (daytime vs evening) will have an impact on which combination of music and message is most effective. using correct vocabulary, explain how to change the design of this experiment to take this into account?

block by time of day. randomly assign all 6 treatments within each block. compare results between treatment groups within each block

how does the block design reduce variability between the different treatment groups and therefore controls for potential confounding by the possible confounding variable?

blocking makes the groups more equalized so that we know the results are based off the treatment not to variable

strata vs blocks

both divide the observations into subgroups, but blocking is associated with experimental design and stratification is associated with random selection

for one kindergarten class in his district, a researcher determines which children already can read simple words and which children cannot upon entering kindergarten. the children are followed until 3rd grade, at which point they are tested to determine the grade level at which they are reading. those children who were reading simple words on entering kindergarten are found to be reading at a higher level than those who could not read simple words on entering kindergarten. the researcher

cannot conclude that being able to read before entering kindergarten is beneficial, as there may be confounding variables in this study

a public opinion poll in Ohio wants to determine whether or not registered voters in the state approve of a measure to ban smoking in all public areas. they select a random sample of five countries and poll all registered voters in each country by asking whether they approve or disapprove of the measure. this is an example of

cluster sample

multistage sampling

combines two or more sampling methods

to determine the proportion of each color of M&Ms, you buy 10 packs at your local grocery store and count how many there are of each color. this is an example of

convenience sampling

does caffeine improve exam performance? suppose all students in the 8:30 section of a course are given a "treatment" (2 cups of coffee) and all students in the 9:30 section are not permitted to have any caffeine before a mid-term exam. the response variable in this study is

exam performance

the 24 hour customer service call center for a major electronics manufacturer is trying to determine how to keep customers who are on hold as happy as possible. they want to examine whether the type of music they play while customers are on hold and whether or not there is a periodically repeated recorded message have an impact on customer satisfaction. they plan to randomly select customers who are on hold and play one of three different types of music (smooth jazz, classical, or show tunes) and either play the recorded message or not. after the entire call is over, they will ask the customers to rate their overall customer service experience. suppose the company plans to conduct a completely randomized design. list the experimental units, factors and treatments in this experimental design

experimental units: each customer on hold factors: music and message treatments: IN SHORT the 6 combos of music and message

replication

first we need to perform this experiment on a sufficient number of experimental units. if we base our experiment on the outcomes of just one or a small number of subjects, then the differences between treatment groups could be due to chance

in order to assess the effects of exercise on reducing cholesterol, a researcher took a random sample of fifty people from a local gym who exercised regularly an another random sample of fifty people from the surrounding community who did not exercise regularly. they all reported to a clinic to have their cholesterol measured. the subjects were unaware of the purpose of the study, and the technician measuring the cholesterol was not aware of whether or not subjects exercised regularly. which of the following best describes the inferences the researcher can make based on his results?

he can make inferences about the population from which the samples were taken, but not about cause and effect

what is true about a simple random sample using a random digit table?

if we use another list of random digits to select the sample, the result obtained with the list actually used would be just as likely to be selected as any other set of three names

random sampling

involves using a chance process to determine which members of a population are included in the sample

levels

just as an explanatory variable may have several levels, factor in an experiment may also have several values and we refer to them as levels

an experiment compares the taste of a new spaghetti sauce with the taste of a commercially successful sauce readily available in grocery stores. each of a number of tasters tastes both sauces (in random order) and says which tastes better. this is called a

matched pairs design

100 volunteers who suffer from severe depression are available for a study. 50 are selected at random and are given a new drug that is thought to be particularly effective in treating severe depression. the other 50 are given an existing drug for treating severe depression. a psychiatrist evaluates the symptoms of all volunteers after four weeks in order to determine if there has been substantial improvement in the severity of the other depression. the study would be double blind if

neither the volunteers nor the psychiatrist knew which treatment any person had received

your school will send a delegation of 35 seniors to a student life convention. 200 girls and 150 boys are eligible to be chosen. a sample of 20 girls and a separate sample of 15 boys are each selected randomly to attend the convention. is this an SRS? explain.

no in an SRS they would have had an equal chance

simple random sampling is A. reduces bias resulting from poorly worded questions B. offsets bias resulting from under coverage and non response C. reduces bias resulting from behavior the interviewer exhibits while asking questions D. reduces variability

none of the above

placebo effect

people who feel better simply due to the fact that they have received treatment even though the treatment may have no real medical benefit

the schools newspaper asked you to contact 50 of the 1200 students at the school to gather information about student opinions regarding food at your school's cafeteria. you decide to randomly select 50 students from B lunch. describe the population and the sampling frame for you study

population: 1200 students at the school sampling frame: all students in B lunch

prospective study

researchers follow subjects collecting data as events unfold and then look for associations between explanatory and response variables

retrospective studies

researches look at data from the subjects past and then look for associations between explanatory and response variables from that data

what are the two types of observational studies?

retrospective and prospective studies

a candidate for mayor of Dallas calls 1,000 people chosen at random from the city telephone directory; 850 of them respond. What are the sampling frame and the sample in this example?

sampling frame (the "list" your're choosing from): the telephone directory. sample: the 850 people who respond

100 volunteers who suffer from severe depression are available for a study. 50 are selected at random and are given a new drug that is thought to be particularly effective in treating severe depression. the other 50 are given an existing drug for treating severe depression. a psychiatrist evaluates the symptoms of all volunteers after four weeks in order to determine if there has been substantial improvement in the severity of the other depression. the factor in this study is

the drug

does caffeine improve exam performance? students in an 8:30 section of a course are randomly assigned to a treatment group (two cups of coffee), or a control group (two cups of decaffeinated coffee). the coffee is so bad that students cannot tell whether they are in the treatment or the control group. as it turns out, students in both groups do better on the exam that students in the 9:30 section, who weren't given anything. this could be the result of

the placebo effect

a sportswriter wants to know how strongly Lafayette residents support the local minor league baseball team, the Lafayette Leopards. he stands outside the stadium before a game and interviews the first 20 people who enter the stadium. the newspaper asks you to comment on their survey of local opinion. You say:

this is a convenience sample. it will almost certainly overestimate the level of support among all Lafayette residents

bias

to underestimate or very likely to overestimate the value you want to know

a church group interested in promoting volunteerism in a community chooses an SRS of 200 community addresses and send members to visit these addresses during weekday working hours to inquire about the residents' attitudes toward volunteer work. sixty percent of all respondents say that they would be willing to donate at least an hour a week to some volunteer organization. bias is present in this sample design. identify the type of bias involved in this example by name and explain why you think the sample results obtained are different from the population.

under coverage and non response is present because if the people are home during a week day working hours then they will have more time to volunteer, overestimating how many hours the community as a whole would be willing to volunteer

the 24 hour customer service call center for a major electronics manufacturer is trying to determine how to keep customers who are on hold as happy as possible. they want to examine whether the type of music they play while customers are on hold and whether or not there is a periodically repeated recorded message have an impact on customer satisfaction. they plan to randomly select customers who are on hold and play one of three different types of music (smooth jazz, classical, or show tunes) and either play the recorded message or not. after the entire call is over, they will ask the customers to rate their overall customer service experience. many utility companies have introduced programs to encourage energy conservation among their customers. an electric company considers placing electronic meters in households to show what the cost would be if the electricity use at that moment continues for a month. it randomly assigns these meters to 100 of its customers for a year and then compares the average electricity use decreased by 10% to their electricity use the previous year. Result: the customers average electricity use decreased by 10% (a statistically significant amount). using correct vocab, explain why this is not evidence that the use of the electronic meters caused customers to decrease their electricity use. provide an example

there could be confounding. maybe conditions require less electricity use this year for these customers and that's whats reducing electricity not the meters

12 people who suffer from chronic fatigue syndrome volunteer to take part in an experiment to see if shark fin extract will increase ones energy level. 8 of the volunteers are men, and 4 are women. half of the volunteers are to be given shark fin extract twice a day, and the other half are to be given a placebo twice a day. we wish to make sure that four men and two women are assigned to each of the treatments, so we decide to use a block design with the men forming one block and the women the other. a block design is appropriate in this experiment if

we believe men and women will respond differently to treatments

control

we need to control sources of variation (i.e. variables) other than the factors we are testing, so we need to make the conditions as similar as possible for all the treatment groups. this helps to ensure that the only differences in the treatment groups are the combinations of factors and levels being tested. if we have that level of control then we can say that any observed difference in the response variable is likely due to the treatments being tested

the schools newspaper asked you to contact 50 of the 1200 students at the school to gather information about student opinions regarding food at your school's cafeteria. you suspect there is a big difference between the opinions of the 400 males and 800 females that make up the student population when it comes to cafeteria food. identify a sampling method by name that takes into account this potentially important variable and explain the advantages of this method in context

you may use stratified sampling which will take into account the proportion of males vs females. there will be a strata of male and female chosen equal to the 400:800 population to prevent more of one gender from being chosen