Stats CH 1

What is a frame?

A frame is a list of the individuals in the population being studied.

What is an observational​ study? What is a designed​ experiment? Which allows the researcher to claim causation between an explanatory variable and a response​ variable? What is an observational​ study? Which allows the researcher to claim causation between an explanatory variable and a response​ variable?

An observational study measures the value of the response variable without attempting to influence the value of either the response or explanatory variables. A designed experiment is when a researcher assigns individuals to a certain​ group, intentionally changing the value of an explanatory​ variable, and then recording the value of the response variable for each group. A designed experiment allows the researcher to claim causation between an explanatory variable and a response variable

Define treatment

Any combination of the values of the factors​ (explanatory variables)

Define experimental unit

A​ person, object, or some other​ well-defined item upon which a treatment is applied

In statistical​ studies, researchers want to determine how varying one or more​ _______ variables may impact the value of​ a(n) _______ variable.

In statistical​ studies, researchers want to determine how varying one or more explanatory variables may impact the value of​ a response variable.

Determine the level of measurement of the variable. Monthly temps: 64, 69, 74, 79, and 84 degrees F

Interval

Consider the two questions shown below.​(a) Who is your favorite actor? ​(b) What is the best movie you have seen in the past year?Will the order in which the questions are asked affect the survey​ results? If​ so, what can the pollster do to alleviate this response​ bias?

Yes,question order will affect the survey results. The pollster should alternate the order of the questions given in the questionnaire so that different respondents receive questionnaires with the same questions but different question orderings.

To help assess student learning in her music history ​courses, a music professor at a community college implemented​ pre- and​ post-tests for her music history students. A​ knowledge-gained score was obtained by taking the difference of the two test scores.

What type of experiment?Matched Pair Response Variable?Difference between test scores Treatment- Type of art class

Suppose a surveyor wants to conduct a phone survey about a new song. She plans to take a simple random sample. However, some people are on a do dash not dash call registry. Do you believe this can affect the ability of the surveyor to obtain accurate polling results? If so, how? Choose the correct answer below.

Yes, especially if the people who are on a do dash not dash call registry have a trait that is not accurately represented by the remaining people in the sample

Define placebo

An innocuous​ medication, such as a sugar​ tablet, that​ looks, tastes, and smells like the experimental medication

Two students out of 29 students in a class have red hair.

Parameter, because the data set of all 29 students is a population.

Does the level of octane in gasoline affect gas​ mileage? To answer this​ question, an automotive engineer obtains 45 cars. Fifteen of the cars are​ compact, 15 are full​ size, and 15 are sport utility vehicles​ (SUVs). Design an experiment for the engineer.

Randomized block design

Determine whether the variable is qualitative or quantitative. Nation of origin.

The variable is qualitative because it is an attribute characteristic

The owner of a shopping mall wishes to expand the number of shops available in the food court. She has a market researcher survey the first 80 customers who come into the food court during weekday evenings to determine what types of food the shoppers would like to see added to the food court. Complete parts​ (a) and​ (b) below.

(a) The survey has bias. Determine whether the flaw is due to the sampling method or the survey itself. For biased​ surveys, identify the cause of the error.What is the cause of the​ bias?Sampling bias(b) Suggest a remedy to the problem.Which of the following is the best way to remedy this​ problem?Ask customers throughout the day on both weekdays and weekends.

The survey has bias.​ (a) Determine the type of bias.​ (b) Suggest a remedy.A polling organization conducts a study to estimate the percentage of households that have high- speed Internet access. It mails a questionnaire to 1778 randomly selected households across the country and asks the head of each household if he or she has high dash speed Internet access. Of the 1778 households​ selected, 49 responded.

(a) Which of these best describes the bias in the​ survey?Nonresponse bias How can the bias be​ remedied?The polling organization should try contacting households that do not respond by phone or​ face-to-face.

The survey has bias.​ (a) Determine the type of bias.​ (b) Suggest a remedy.A pro dash evolution advocate wants to estimate the percentage of people who favor teaching only evolution in schools. He conducts a nationwide survey of 1540 randomly selected adults 18 years and older. The interviewer asks the​ respondents,​"Do you favor promoting science by teaching only evolution in schools?

(a) Which of these best describes the bias in the​ survey?Response bias​(b) How can the bias be​ remedied?The interviewer should reword the question.

A school psychologist wants to test the effectiveness of new method of teaching English. She recruits 400 third-grade students and randomly divides hem into two groups. Group 1 is taught by means of the new​ method, while group 2 is taught by traditional methods. The same teacher is assigned to teach both groups. At the end of the​ year, an achievement test is administered and the results of the two groups are compared. Complete parts​ (a) through​ (i) below.

1. What is the response variable in this experiment?The scores on the achievement tests of both group 1 and group 2 2.Is the response variable qualitative or​ quantitative?The response variable is quantitative because it is a measurement 3. Which of the following explanatory variables is manipulated?Method of teaching 4.What are the​ treatments? How many treatments are​ there?The treatments are the new teaching method and the traditional teaching method. There are 2 treatments. 5. How are the factors that are not controlled dealt​ with?random assignment 6. Which group serves as the control group?Group 2 serves as the control group because this group corresponds to the standard method that will be compared to the other method. 7. what type of experimental design is this?Completely randomized design 8. Identify the subject.400 students

What does it mean when a part of the population is​ under-represented?

A part of the population is​ under-represented when it is proportionally smaller in a sample than in its population.

Explain the difference between a population and a sample.

A population is the entire group that is being studied while a sample is a subset of the population that is being studied.

Discuss a possible advantage of offering rewards or incentives to increase response rates. Are there any​ disadvantages?

A possible advantage of offering rewards or incentives to increase response rates is that respondents put more effort into completely and accurately answering the survey questions because they feel obligated. A possible disadvantage of offering rewards or incentives to increase response rates is that the people interested in the rewards or incentives differ from the population in some way that is important to the​ study, causing biased results.

What does it mean when an observational study is​ retrospective? What does it mean when an observational study is​ prospective? What does it mean when an observational study is​ retrospective?

A retrospective study requires that individuals look back in time or require the researcher to look at existing records. A prospective study collects the data over time.

Define simple random sampling

A sample of size n from a population of size N is obtained through simple random sampling if every possible sample of size n has an equally likely chance of occurring. The sample is then called a simple random sample.

Define factor

A variable whose effect on the response variable is to be assessed by the experimenter

A​ quality-control manager randomly selects 30 bottles of ketchup that were filled on June 3 to assess the calibration of the filling machine. What is the population in the​ study? Sample?

All bottles of ketchup produced in the plant on June 3. The 30 bottles of ketchup selected in the plant on June 3.

To determine customer opinion of their safety features, Daimler−Chrysler randomly selects 70 service centers during a certain week and surveys all customers visiting the service centers.

Cluster

A _____ is obtained by dividing the population into groups and selecting all individuals from within a random sample of the groups.

Cluster sample

Researchers wanted to determine if there was an association between the level of happiness of an individual and their risk of breast cancer. The researchers studied 1647 people over the course of 15 years. During this 15​-year ​period, they interviewed the individuals and asked questions about their daily lives and the hassles they face. In​ addition, hypothetical scenarios were presented to determine how each individual would handle the situation. These interviews were videotaped and studied to assess the emotions of the individuals. The researchers also determined which individuals in the study experienced any type of breast cancer over the 15​-year period. After their​ analysis, the researchers concluded that the happy individuals were less likely to experience breast cancer. In the​ report, the researchers stated that​ "the research team also​ hasn't ruled out that a common factor like genetics could be causing both the emotions and the breast cancer". Explain what this sentence means. Choose the correct answer below.

Cohort study because the information collected was observed over a long period of time. The response variable is whether or not breast cancer was contracted because it is the variable of interest. The explanatory variable is the level of happiness because it affects the other variable. The researchers may be concerned with confounding that occurs when the effects of two or more explanatory variables are not separated or when there are some explanatory variables that were not considered in a​ study, but that affect the value of the response variable.

Explain what is meant by confounding. What is a lurking​ variable? What is a confounding​ variable? What is meant by​ confounding?

Confounding in a study occurs when the effects of two or more explanatory variables are not separated.​ Therefore, any relation that may exist between an explanatory variable and the response variable may be due to some other variable or variables not accounted for in the study. A lurking variable is an explanatory variable that was not considered in a​ study, but that affects the value of the response variable in the study. In​ addition, lurking variables are typically related to explanatory variables in the study. A confounding variable is an explanatory variable that was considered in a study whose effect cannot be distinguished from a second explanatory variable in the study.

What is a​ cross-sectional study? What is a​ case-control study? Which is the superior observational​ study? Why?

Cross-sectional studies are observational studies that collect information about individuals at a specific point in time or over a very short period of time. Case-control studies are observational studies that are​ retrospective, meaning that they require individuals to look back in time or require the researcher to look at existing records. Neither study is always the superior to the other. Both have advantages and disadvantages that depend on the situation.

A poll is being conducted at a pet store to obtain a sample of the population of an entire country. What is the frame for this type of sampling? Who would be excluded from the survey and how might this affect the results of the survey?(a) What is the frame for this type of sampling? Who would be excluded from the survey and how might this affect the results of the survey?

D. the entire population of the country&A. Any person who does not like pets is excluded. This could result in sampling bias due to undercoverage.

In​ statistics, results are always reported with​ 100% certainty. Choose the correct answer below.

False. In​ statistics, results are not reported with​ 100% certainty. Because statistical studies draw on​ samples, and because there is variation within​ groups, results cannot be reported with​ 100% certainty.

Statistical studies are not concerned with understanding the sources of variability in​ data, only with describing the variability in the data. Choose the correct answer below.

False. Statistical studies are concerned with both describing the variability in the data and understanding the sources of variability in data. Understanding the sources allows researchers to control it and reach better conclusions.

When obtaining a stratified​ sample, the number of individuals included within each stratum must be equal.

False. Within stratified​ samples, the number of individuals sampled from each stratum should be proportional to the size of the strata in the population.

Surveys tend to suffer from low response rates. Based on past​ experience, a researcher determines that the typical response rate for an​ e-mail survey is 20​%. She wishes to obtain a sample of 200 ​respondents, so she​ e-mails the survey to 2000 randomly selected​ e-mail addresses. Assuming the response rate for her survey is 20​%, will the respondents form an unbiased​ sample? Explain.

No. The survey still suffers from undercoverage​ (sampling bias), nonresponse​ bias, and potentially response bias.

Determine the level of measurement of the variable. Dress color

Nominal

Distinguish between nonsampling error and sampling error.

Nonsampling error is the error that results from​ undercoverage, nonresponse​ bias, response​ bias, or​ data-entry errors. Sampling error is the error that results because a sample is being used to estimate information about a population.

As part of a college literature​ course, students must read three classic works of literature from the provided list. Write a short description of the processes that can be used to generate a simple random sample of three books. Obtain a simple random sample of size 3 from this list (9 books total).

Number the books from 1 to 9 and use a random number generator to produce 3 different numbers from 1 to 9 that correspond to the books selected. OR List each book on a separate piece of​ paper, place them all in a​ hat, and pick three.

What does it mean when sampling is done without​ replacement?

Once an individual is​ selected, the individual cannot be selected again.

Determine the level of measurement of the variable. The rankings of songs in the top 100

Ordinal

A marketing research firm wants to determine the most effective method of promoting a political party​: ​print, radio,​ television, or online. They recruit 390 volunteers to participate in the study. The researcher segments the volunteers by age. Of the 390 ​volunteers, 80 are under age 20​, 60 are 20 dash 39 years old​, 130 are 40 dash 59 years old​, and 120 are 60 years old or older. The volunteers from each group are randomly assigned to either the print advertising​ group, the radio​ group, the television​ group, or the online group. Each group is exposed to the advertising. After 2 hours​, a recall exam is given with the proportion of correct answers recorded. Complete parts​ (a) through​ (f) below.

Randomized block design ​(b) What is the response variable in this​ experiment? The score on the recall exam ​(c) What is the explanatory variable that is manipulated and set at various​ levels? The type of advertising ​(d) How many levels of treatment are​ there? 4 ​(e) What variable serves as the​ block? ​The ages of the subjects

What is replication in an​ experiment?

Replication is applying each treatment to more than one experimental unit.

A radio station asks its listeners to call in their opinion regarding the closing of fire stations in the city.

Sample response: A convenience sample is used. The sample could be biased because it limits the population to listeners of that radio station at a certain time. Callers may be more likely to have a strong opinion on the issue.

Suppose that a radio station predicted that Candidate A would defeat Candidate B in a certain election. They conducted a poll of its listeners with a response rate of 24%. ON the basis of the results, the radio station predicted that Candidate A would win with 57% of the popular vote. However, Candidate B won the election with about 62% of the popular vote. At the time of this poll, most listeners of the station belonged to the party of candidate A. Name two biases that led to this incorrect prediction.

Sampling​ bias: Using an incorrect frame led to undercoverage. Nonresponse​ bias: The low response rate caused bias.

Sony wants to administer a satisfaction survey to its current customers. Using their customer​ database, the company randomly selects 30 customers and asks them about their level of satisfaction with the company.

Simple random

Choose the correct answer.

Statistics is the science of​ collecting, organizing,​ summarizing, and analyzing information to draw a conclusion and answer questions. In​ addition, statistics is about providing a measure of confidence in any conclusions.

A(n) ______________ is obtained by dividing the population into homogeneous groups and randomly selecting individuals from each group.

Stratified sample

To determine her stress level, Debra divides up her day into three​ parts: morning,​ afternoon, and evening. She then measures her stress level at 3 randomly selected times during each part of the day.

Stratified sampling

To estimate the percentage of defects in a recent manufacturing​ batch, a quality control manager at IBM selects every 18th computer that comes off the assembly line starting with the second until she obtains a sample of 60 computers. What type of sampling is this?

Systematic

Which sampling method does not require a​ frame?

Systematic

​Generally, the goal of an experiment is to determine the effect that the treatment will have on the response variable.

T

Thinking about how the tariff issue might affect your vote for major​ offices, would you vote only for a candidate who shares your views on tariffs or consider a​ candidate's position on tariffs as just one of many important​ factors? [rotated] Why is it important to rotate the two choices presented in the​ question?

The choices need to be rotated to minimize response biases

Define confounding

The effect of two factors​ (explanatory variables on the response​ variable) cannot be distinguished.

Define response variable.

The quantitative or qualitative variable for which the experimenter wishes to determine how its value is affected by the explanatory variable

First grade students are randomly divided into two groups. One group is given fruit and the other candy for lunch. After lunch, each group is given an attention test to compare hyperactivity.

The study is an experiment because the researchers control one variable to determine the effect on the response variable.

Determine whether the study depicts an observational study or an experiment. A study is conducted to determine if there is a relationship between stomach cancer and alcohol consumption. Everyone treated at a hospital for stomach cancer was asked about their alcohol consumption. Does the description correspond to an observational study or an​ experiment?

The study is an observational study because the study examines individuals in a sample, but does not try to influence the response variable.

A poll is conducted by a school's English department in which eighth grade students are asked if they prefer to be in their English class or their math class.

The study is an observational study because the study examines individuals in a sample, but does not try to influence the response variable.

Batting average of 0.366. Is the value a parameter or a statistic?

The value is a parameter because the career at-bats of a baseball player are a population.

Following the election, 18% of the governors of all 50 areas of a country were female.

The value is a parameter because the governors of all 50 area of a country are a population.

Determine whether the quantitative variable is discrete or continuous. Length of rock song.

The variable is continuous because it is not countable.

Determine whether the quantitative variable is discrete or continuous. Number of cars owned.

The variable is discrete because it is countable.

Determine whether the quantitative variable is discrete or continuous. Points scored in a college basketball game.

The variable is discrete because it is countable.

Determine whether the variable is qualitative or quantitative. Model of car driven.

The variable is qualitative because it is an attribute characteristic

To research the claim that green tea lowers LDL​ (so-called bad)​ cholesterol, you ask a random sample of individuals to divulge whether they are regular green tea users or not. You also obtain their LDL cholesterol levels.​ Finally, you compare the LDL cholesterol levels of the green tea drinkers to those of the​ non-green tea drinkers. Explain why this is an observational study.

This is an observational study because there is no intent to manipulate the explanatory​ variable, whether the individual is a green tea drinker or not. Lurking variables: Genetics, age, gender, exercise, adn diet ​(c)​ Suppose, instead of surveying individuals regarding their​ tea-drinking habits, you decide to conduct a designed experiment. You identify 120 volunteers to participate in the study and decide on three levels of the​ treatment: a​ placebo, one cup of green tea​ daily, two cups of green tea daily. The experiment is to run for one year. The response variable will be the change in LDL cholesterol for each subject from the beginning of the study to the end. What type of experimental design is​ this? Completely randomized design ​(e) What is the​ factor? Is it qualitative or​ quantitative? the amount of green tea daily, qualitative. Control the factors of: Diet and exercise Randomly assign the experimental units to treatment groups. This will mute the effect of variation attributable to the explanatory variables that are not controlled. Then any difference in the value of the response variable among the different treatment groups is a result of differences in the level of the treatment. Any difference in the change in the response variable cannot be attributed to the treatment level. It may be the exercise that causes the change in the response variable.

Suppose three different individuals conduct the same statistical​ study, such as estimating the average commute time of students at a college. It is possible that all three studies end up with different results. Choose the correct answer below.

True. Statistical studies typically look at samples rather than entire populations. Since each study is likely to draw different​ samples, it is quite possible that each study ends up with different​ results, due to variability in the data

Researchers studied 600 people and matched their personality type to when in the year they were born. They discovered that the number of people with a​ "cyclothymic" temperament, characterized by​ rapid, frequent swings between sad and cheerful​ moods, was significantly lower in those born in the winter. The study also found that those born in the autumn were less likely to be depressive​, while those born in spring were less likely to be irritable. Complete parts​ (a) through​ (e) below. ​(a) What is the research question the study​ addresses? (b) What is the sample? (c) What type of variable is the season in which you were born? (d) What can be said about individuals born in winter?

a: Does season of birth affect mood? b: The 600 people in the study c: Qualitative, nominal d: People born in winter are less likely to have mood swings

Grouping together similar experimental units and then randomly assigning the experimental units within each group to a treatment is called

blocking

During every election in a particular​ region, pollsters conduct exit polls to help determine which candidate people voted for. During the most recent​ election, pollsters incorrectly predicted candidate A the winner over candidate B. When asked how this error could have​ happened, the pollsters cited interviewer error due to the fact that in some precincts that favoredcandidate B, interviewers were denied access to voters selectedin the sample. ​Plus, the interviewers made many mistakeswhen recording the responses of the respondents. In​ addition, the method of selecting individuals to be interviewed led to selecting alower proportion of female ​voters, and candidate B was favored byfemales. Explain which nonsampling errors led to the incorrect conclusion regarding the election.

nonresponse bias is a nonsampling error that contributed to the incorrect conclusion because the individuals who were selected for polling but were not able to respond voted differently than those who did respond to the polling.

Numerical summary of a population

parameter

Numerical summary of a sample

statistic

To determine if topiramate is an effective treatment for alcohol​ dependence, researchers conducted a​ 14-week trial of 371 men and women aged 18 to 65 years diagnosed with alcohol dependence. In this​ doubleblind, randomized,​ placebo-controlled experiment, subjects were randomly given either 300 milligrams​ (mg) of topiramate​ (183 subjects) or a placebo​ (188 subjects)​ daily, along with a weekly compliance enhancement intervention. The variable used to determine the effectiveness of the treatment was​ self-reported percentage of heavy drinking days. Results indicated that topiramate was more effective than placebo at reducing the percentage of heavy drinking days. The researchers concluded that topiramate is a promising treatment for alcohol dependence. Complete parts​ (a) through​ (f).

​(a) What does it mean for the experiment to be​ placebo-controlled? The experiment will have a control group that takes a​ placebo, which is a innocuous​ medication, such as a sugar tablet. This control group serves as a baseline treatment that can be used to compare to the group that is actually taking the medication. What does it mean for the experiment to be​ double-blind? Neither the subject nor the researcher knows which treatment the subject is receiving. The experiment is​ double-blind so that the subjects receiving the medication do not behave differently and so the individual monitoring the subjects does not treat those receiving medication differently from those receiving a placebo. ​(c) What does it mean for the experiment to be​ randomized? It means that the subjects are randomly assigned to take either the topiramate or the placebo. The population is all​ 18-65 year olds with alcohol dependence. The sample is 371 men and women aged 18 to 65 years diagnosed with alcohol dependence What are the treatments? 300 mg of topiramate or a placebo​ daily, and a weekly compliance enhancement intervention What is the response variable? Percentage of heavy drinking days.

Researchers wish to know if there is a link between hypertension​ (high blood​ pressure) and consumption of sugar. Past studies have indicated that the consumption of fruits and vegetables offsets the negative impact of sugar consumption. It is also known that there is quite a bit of​ person-to-person variability as far as the ability of the body to process and eliminate sugar. ​However, no method exists for identifying individuals who have a higher ability to process sugar. It is recommended that daily intake of sugar should not exceed 5600 milligrams​ (mg). The researchers want to keep the design​ simple, so they choose to conduct their study using a completely randomized design. Complete parts​ (a) through​ (c).

​(a) What is the response variable in the​ study? Blood pressure ​(b) Name three factors that have been identified. Daily consumption of fruits and vegetables, Daily consumption of sugar, and ​Body's ability to process sugar (c) For each factor​ identified, determine whether the variable can be controlled or cannot be controlled. Blood pressure is not a factor. Daily consumption of sugar can be controlled. Daily consumption of fruits and vegetables can be controlled. ​Body's ability to process sugar cannot be controlled. Age is not a factor. Gender is not a factor. If a factor cannot be​ controlled, what should be done to reduce variability in the response​ variable? Experimental units should be randomized to each treatment group.

A physician wanted to compare two types of headache relief. One type is medication and the other is using pressure points. It is a common belief that medication relieves pain faster. This belief is tested by having 10 migraine sufferers compare both types of pain relief and record their observations on a standardized scale of response. A coin flip was used to determine which type of headache relief each individual would try first. Results indicated that there was no difference in the two types of pain relief. Complete parts​ (a) through​ (f) below.

​(a) What type of experimental design is​ this? Matched pair ​(b) What is the response variable in this​ study? The recorded observations ​(c) What is the factor that is set to predetermined​ levels? What is the​ treatment? The factor is the type of pain relief.The treatments are medication and using pressure points. ​(d) Identify the experimental units. Choose the correct answer below. The migraine sufferers ​(e) Why is a coin used to decide the​ headache relief each individual would try first? To eliminate bias as to which pain relief was used first

Researchers wanted to test the effectiveness of a new drug therapy for treating patients with strokes. To do​ this, they identified 120 patients with a diagnosis of strokes. Patients were randomly assigned to one of three treatment groups. Forty patients were randomly assigned to receive the new drug​ therapy, another 40 received the older drug​ therapy, and the final 40 received a placebo therapy. To measure the effectiveness of the​ treatment, researchers scored each patient on a standardized rating scale for strokes. After collecting and comparing the scores for the three treatment​ groups, the researchers concluded that the new drug therapy is significantly more effective than both the older drug therapy and the placebo therapy in the treatment of strokes. Complete parts​ (a) through​ (f).

​(a) What type of experimental design is​ this? Completely randomized design What is the population being studied? All patients with a diagnosis of strokes ​(c) What is the response variable in this​ study? The score on the standardized rating scale for strokes ​(d) What are the​ treatment(s)? The new drug​ therapy, the older drug​ therapy, and the placebo therapy ​(e) Identify the experimental units. Choose the correct answer below. The 120 patients with a diagnosis of strokes

A simple random sample is always preferred because it obtains the same information as other sampling plans but requires a smaller sample size?

​False, because other sampling techniques may provide more information for less cost than a simple random sample.

When conducting a cluster​ sample, it is better to have fewer clusters with more individuals when the clusters are heterogeneous.

​True, because when the clusters are​ heterogeneous, they are scaled down versions of the population.