Stats CH 1

What is a confounding​ variable?

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 designed​ experiment?

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.

experimental units

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

Determine whether the variable is qualitative or quantitative. The number of megabytes of RAM in a computer Is the variable qualitative or​ quantitative?

The variable is quantitative because it is a numerical measure.

sampling bias

a flawed sampling process that produces an unrepresentative sample

Placebo

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

Researchers wanted to determine if there was an association between the level of happiness of an individual and their risk of diabetes The researchers studied 1604 people over the course of 13 years. During this 13 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 diabetes over the 13year period. After their​ analysis, the researchers concluded that the happy individuals were less likely to experience diabetes Complete parts​ (a) through​ (c).

-Cohort overtime -The response variable is whether or not diabetes was contracted, because it is the variable of interest. The explanatory variable is level of happiness, because it affects the other variable.

Researchers wanted to test the effectiveness of a new drug therapy for treating patients with diabetes. To do​ this, they identified 90 patients with a diagnosis of diabetes. Patients were randomly assigned to one of three treatment groups. Thirty patients were randomly assigned to receive the new drug​ therapy, another 30 received the older drug​ therapy, and the final 30 received a placebo therapy. To measure the effectiveness of the​ treatment, researchers scored each patient on a standardized rating scale for diabetes. 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 diabetes. Complete parts​ (a) through​ (f).

-Completely randomized design -All patients with a diagnosis of diabetes -The score on the standardized rating scale for diabetes -The new drug​ therapy, the older drug​ therapy, and the placebo therapy -The 90 patients with a diagnosis of diabetes -Figure 1

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.

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

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.

-Matched-pairs design -the recorded observations -The factor is the type of pain relief. The treatments are medication and using pressure points -The migraine sufferers -To eliminate bias as to which pain relief was used first -Figure 2

You wonder whether green tea lowers cholesterol. Complete parts​ (a) through​ (h) below. ​(a) 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. -Exercise, Gender, Genetics, Age, Diet -Completely randomized design -Do not allow the subjects to know which level of the treatment they are receiving.​ Also, do not allow the​ researcher(s) giving the treatments to know which level of the treatment they are giving. This is a​ double-blind study. -The factor is the amount of green tea daily. It is qualitative. -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 caused the change in the response variable.

Suppose the size of a population is N= 4000 and the sample size desired is n=11. What value of k should be used to obtain a systematic sample from this​ population?

4000 divided by 11= 363

A professor wants to randomly select 4 students to go to the board. She decides to randomly select the seventh student who enters the classroom and every eighth student after that. Determine the students who will be going to the board. Write down the student numbers.

7, 15, 23, 31

What is a frame?

A list of the individuals in the population being studied

convenience

A newspaper asks its readers to call in their opinion regarding the number of books they have read this month.

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

A prospective study collects the data over time.

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.

random simple 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.

factor

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

Researchers studied 300 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 spring were less likely to be depressive, while those born in autumn were more likely to be excessively positive. Complete parts​ (a) through​ (e) below.

A) Does season of birth affect​ mood? B) The 300 people in the study C) Qualitative, nominal D) People born in winter are less likely to have mood swings. E) Season of birth plays a role in one's temperament

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.

allows the researcher to claim causation between an explanatory variable and a response variable

Designed experiment

What is a lurking variable?

Explanatory variable that was not considered in a study, but that affects the value of the response variable in the study. Related to explanatory variables in the study.

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.

Explain the difference between a​ single-blind and a​ double-blind experiment.

In a​ single-blind experiment, the subject does not know which treatment is received. In a​ double-blind experiment, neither the subject nor the researcher in contact with the subject knows which treatment is received.

what is a superior observational study

Neither study is always the superior to the other. Both have advantages and disadvantages that depend on the situation.

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.

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

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

Confounding

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

treatment

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

response variable

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

7th grade students are randomly divided into 2 groups. 1 group is taught math using traditional techniques. The other is taught math using a reform method. After 1 year each group is given an achievement test to compare proficiency. Is this an observational study or an experiment

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

In a survey of 1,011 people 50 or older, Modifying 73 % with underlined agreed with the statement "I believe in life after death."

The value is a statistic because the 1011 people age 50 or older are a sample

Determine whether the quantitative variable is discrete or continuous. Number of coins in a jar Is the variable discrete or​ continuous?

The variable is discrete because it is countable.

street name-- quantitative or qualitative

The variable is qualitative because it has attributed characteristic

cluster

To determine customer opinion of their check dash in service American Airlines randomly selects 70 flights during a certain week and surveys all passengers on the flights

stratified

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

Identify the​ individuals, variables, and data corresponding to the variables. Determine whether each variable is​ qualitative, continuous, or discrete.

What are the individuals being​ studied? -The​ high-definition television setups A through E. What are the variables and their corresponding data being​ studied? -

An observational study measures the value of the response variable without attempting to influence the value of either the response or explanatory variables.

What is an observational study?

Researchers wanted to determine if having a video game console in the bedroom is associated with obesity. The researchers administered a questionnaire to 357 twelve-year-old adolescents. After analyzing the​ results, the researchers determined that the body mass index of the adolescents who had a video game console in their bedroom was significantly higher than that of the adolescents who did not have a video game console in their bedroom. Complete parts​ (a) through​ (e) below.

a)The researchers administered a questionnaire to obtain their data without trying to influence an explanatory variable of the study. b) Cross sectional study c)The response variable is the body mass index of the adolescents. The response variable is quantitative. d) The explanatory variable is whether the adolescent has a video game console in the bedroom or not. e)Yes. For​ example, possible lurking variables might be eating habits and the amount of exercise per week. f)In the​ report, the researchers​ stated, "These results remain significant after adjustment for socioeconomic​ status." What does this​ mean? The researchers made an effort to avoid confounding by accounting for potential lurking variables.

response bias

anything in a survey design that influences responses

nonresponse bias

bias introduced to a sample when a large fraction of those sampled fails to respond

width of plank of wood--continuous or discrete?

continuous

Method of measurement for election years (1988, 1992, 1996, 2000, and 2004)

interval

cluster sample

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

It is extremely important for a researcher to clearly define the variables in a study because this helps to determine the type of analysis that can be performed on the data. For​ example, if a researcher wanted to describe baseball players based on jersey number what level of measurement would the variable ​"jersey number" be? Now suppose the researcher felt that certain players who were of lower caliber received higher numbers. Does the level of measurement of the variable​ change? If​ so, how?

nominal yes it changes to ordinal

Determine the level of measurement of the variable. Livability rankings for cities

ordinal

ranks of scored in a tournament

ordinal

Amount of money won in a lottery--quantitative or qualitative

quantitative because it is a numerical measure

To estimate the percentage of defects in a recent manufacturing​ batch, a quality control manager at Daimler minus Chrysler selects every 10th van that comes off the assembly line starting with the ninth until she obtains a sample of 40 vans

systematic

volume of a sound-- continuous or discrete

the variable is continuous because it is not countable

random simple sample

wants to administer a satisfaction survey to its current customers. Using their customer​ database, the company randomly selects 70 customers and asks them about their level of satisfaction with the company.

A news service conducted a survey of 1018 adults ages 18 years or older in a certain​ country, August 31-September 2, 2015. The respondents were​ asked, "Of every tax dollar that goes to the federal​ government, how many cents of each dollar would you say are​ wasted?" The four possible responses are that the federal government wastes less than 10​ cents, between 11 cents and 25​ cents, between 26 cents and 50​ cents, or 51 cents or more. Of the 1018 individuals surveyed, 35% indicated that 51 cents or more is wasted. The news service reported that 35% of all adults in the country 18 years or older believe the federal government wastes at least 51 cents of each dollar​ spent, with a margin of error of 5% and a 99% level of confidence. Complete parts ​(a) through​ (e) below.

​(a) What is the research​ objective? To determine the percent of adults in the country who believe the federal government wastes 51 cents or more of every dollar ​(b) What is the​ population? Adults in the country aged 18 years or older ​(c) What is the​ sample? The 1018 adults in the country that were surveyed ​(d) List the descriptive statistics. Choose the correct answer below. 35% of the individuals surveyed indicated that 51 cents or more is wasted. ​(e) What can be inferred from this​ survey? The news service is 99% confident that the percentage of all adults in the country who believe the federal government wastes 51 cents or more of every dollar received is between 30% and 40%.

What is a case-control study?

​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.

What is a cross-sectional study?

​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.

Researchers wanted to know if there is a link between proximity to​ high-tension wires and the rate of leukemia in children. To conduct the​ study, researchers compared the rate of leukemia for children who lived within​ 1/2 mile of​ high-tension wires to the rate of leukemia for children who did not live within​ 1/2 mile of​ high-tension wires. The researchers found that the rate of leukemia for children near​ high-tension wires was higher than the rate for those not near​ high-tension wires. Can the researchers conclude that proximity with​ high-tension wires causes leukemia in​ children?

​No, because this is an observational study.