Stats 1090 Chapter 1

Clustered Sampling

- breaks up the population into similar groups & randomly select 1 or more of these groups as our sample. -dividing the population into​ groups, or​ clusters, and selecting some of these clusters at random.​ Then, researchers obtain the sample by choosing all the members within each of the selected clusters.

In a comparison of gasoline with different octane ratings​, 34 vans are driven with 87 octane gasoline​, while 29 sport utility vehicles are driven with 91 octane gasoline. After being driven for 150 ​miles, each vehicle is rated on quality of performance. The researchers doing the performance quality ratings are aware of which vehicles receive 87 octane gasoline and which receive 91 octane gasoline. Explain how the problems could be avoided. Select all that apply.

-Differences in the gasoline consumption measurements can be correctly attributed to octane level by using 87 octane gasoline in half of the subcompact cars and half of the vans and by using 91 octane gasoline in the other vehicles. -The size of the groups should be increased to eliminate the possibility of a biased sample.

Some cruise ship passengers are given magnetic​ bracelets, which they agree to wear in an attempt to eliminate or diminish the effects of motion sickness. Others are given similar bracelets that have no magnetism. What type of study is​ this? What are the variables of​ interest?

-Experiment. The variable of interest is whether the passenger experienced motion sickness. -This is an experiment because some subjects were given a treatment of magnetic bracelets. The variable of interest is whether the passenger experienced motion sickness.

In testing the effectiveness of a new​ vaccine, suppose that researchers used males for the treatment group and females for the placebo group. How would it affect such an​ experiment?

-If males are given the treatment and females are given​ placebos, a researcher would not know whether effects are due to the treatment or the sex of the participant. -Any differences between the effects observed in the control group and the treatment group could be attributed either to the vaccine or to the sex of the participants.

A​ nine-year-old tested professional touch therapists. Using a cardboard​ partition, she held a hand above one of the​ therapist's hands, and the therapist was asked to identify the hand that was chosen. What type of study is​ this? What are the variables of​ interest?

-Observational study. The variable of interest is the result of either correct or incorrect for each trial. -This is an observational study because the subjects were tested but were not given any treatment. The variable of interest represents the results of either correct or incorrect for each trial.

A physician conducts a clinical trial of the effectiveness of running as a treatment for back pain. One group of 57 randomly selected participants undergoes the running treatment while a control group of 55 randomly selected participants does not. The researchers doing the measurements of back pain are aware of which participants receive the running treatment and which do not receive it. Identify any problems that are likely to cause confounding. Select all that apply.

-There is likely to be a placebo effect in this study because the subjects know whether or not they are running. -There is likely to be experimenter effect in this study because the researchers making the back pain measurements will influence the participants run and which participants don't run.

In a comparison of gasoline with different octane ratings​, 34 vans are driven with 87 octane gasoline​, while 29 sport utility vehicles are driven with 91 octane gasoline. After being driven for 150 ​miles, each vehicle is rated on quality of performance. The researchers doing the performance quality ratings are aware of which vehicles receive 87 octane gasoline and which receive 91 octane gasoline. Identify any problems that are likely to cause confounding and explain how the problems could be avoided. Identify any problems that are likely to cause confounding. Select all that apply.

-There is likely to be an some confounding in this study because the researchers making the performance quality ratings will be influenced by knowing which vehicles receive 87 octane gasoline and which vehicles receive 91 octane gasoline. -If there are differences in the amount of performance quality​, there is no way to know if the differences are attributable to the​ treatments, 87 or 91 octane​, or the type of​ vehicle, van or sport utility vehicle.

A physician conducts a clinical trial of the effectiveness of running as a treatment for back pain. One group of 57 randomly selected participants undergoes the running treatment while a control group of 55 randomly selected participants does not. The researchers doing the measurements of back pain are aware of which participants receive the running treatment and which do not receive it. Explain how the problems could be avoided. Select all that apply.

-Unfortunately, there is no way to eliminate the placebo effect in this study. -The researchers doing the measurements should not be aware of which participantsThe researchers doing the measurements should not be aware of which participants receive the treatment and which do not.

Cluster sampling and stratified sampling both involve selecting subjects in subgroups of the population. What is the difference between those two types of​ sampling?

-With cluster​ sampling, all members of randomly selected subgroups​ (or clusters) are​ selected, but with stratified​ sampling, samples from each of the different subgroups​ (or strata) are selected.

What is a population​ parameter?

-a numerical value describing some attribute of a population. -number that describes a population.

What is a sample​ statistic?

-a numerical value describing some attribute of a sample and are found by consolidating or summarizing the raw data. -numerical summary of the sample

What is a​ sample?

-a portion of the entities of interest that the researcher uses to gather data. -a subset of the population from which data are actually obtained

Stratified Sampling

-break the population up into distance groups & randomly select from within these groups as our sample. -used when there is concern about differences among​ subgroups, or​ strata, within a population. Researchers first identify the strata and then draw a random sample within each stratum. The total sample consists of all the samples from the individual strata.

What is a​ population?

-the entire group of entities of interest to a researcher. -entire group of individuals(not always people) that we want to learn about

What is a​ census, what is a​ sample, and what is the difference between​ them?

A census is the collection of data from every member of the​ population, but a sample is the collection of data from only a part of the population.

What is the difference between a sample statistic and a population​ parameter?

A population parameter is frequently impractical or impossible to find for large​ populations, however a sample statistic is often easier to find and provides a reasonable approximation to the population parameter.

What is the difference between a population and a​ sample?

A sample is only a part of a complete population.

In a survey of 1,002 ​people, 711 ​(or 71​%) said that they voted in a particular presidential election. The margin of error for this survey was 33 percentage points.​ However, actual voting records show that only 60​% of all eligible voters actually did vote. Does this imply that people lied when they responded in the​ survey? Explain.

Based on the​ survey, the actual percentage of voters is expected to be between 68% and 74​%, which does not include the 60​% value based on actual voter results. If the survey was conducted​ properly, it is unlikely that its results would be so different from the actual​ results, implying either that respondents intentionally lied to appear favorable to the pollsters or that their memories were inaccurate.

To determine customer opinion of their pricingpricing​, AmtrakAmtrak randomly selects 130 trains during a certain week and surveys all passengers on the trains. What type of sampling is​ used?

Cluster Sampling

A researcher plans to investigate the belief that people are more comfortable in the summer sun when they wear clothing with light colors instead of clothing with dark colors. Is it easy to implement blinding in this​ case? Explain.

No, because the color of clothing that a person is wearing is usually quite obvious. The study would have to be carefully designed so that neither the subject nor the researchers could discern the shade of the​ participants' clothing.

A political scientist randomly selects 33 of the 202 representatives currently serving in the legislative body of a​ government, then finds their political party affiliations. Identify the sampling method.

Simple Random Sampling

Nissan wants to administer a satisfaction survey to its current customers. Using their customer​ database, the company randomly selects 60 customers and asks them about their level of satisfaction with the company. What type of sampling is​ used?

Simple Random Sampling

A political scientist randomly selects 33 of the 202 representatives currently serving in the legislative body of a​ government, then finds their political party affiliations. Comment on whether it is likely that the sample is representative of the population.

Since the sample size is very​ small, it is not likely to be representative of the population.

To determine her heart rate​, Carolyn divides up her day into three​ parts: morning,​ afternoon, and evening. She then measures her heart rate at 44 randomly selected times during each part of the day. What type of sampling is​ used?

Stratified Sampling

A political scientist randomly selects 33 of the 202 representatives currently serving in the legislative body of a​ government, then finds their political party affiliations. Identify the sample.

The 33 randomly selected representatives

Fifty adult men in the United States are randomly selected and measured for their body mass index​ (BMI). Based on that​ sample, it is estimated that the average​ (mean) BMI for men is 25.0​, with a margin of error of 3.3. Use the given statistic and margin of error to identify the range of values​ (confidence interval) likely to contain the true value of the population parameter.

The range of values likely to contain the population parameter is from (22.1) to (28.9). Confidence Interval: (Estimate - Margin of Error, Estimate+ Margin of Error)

Decide whether the statement below makes sense or does not make sense. Explain. There is no doubt that Johnson won the​ election, because an exit poll showed that she received​ 54% of the vote and the margin of error is only 3 percentage points.​ (Assume that all the people in the poll answered​ truthfully.)

The statement does not make​ sense, because there is always a possibility that a population parameter is not contained in the confidence interval determined by a sample statistic and a margin of error.

Decide whether the statement makes sense​ (or is clearly​ true) or does not make sense​ (or is clearly​ false). Explain. The sample study must have been​ biased, because it concluded that​ 90% of Americans are more than 6 feet tall.

The statement makes sense. It is obvious that the percentage of Americans more than 6 feet tall is well under​ 90%. ​ Therefore, the study must have used a biased sample.

State the type of study described below. In a study of a gender selection method developed by an institute, 150 couples using the method had 117 baby boys and 33 baby girls. Another group of couples, that did not receive the procedures of the method, had about half girls. The couples were not told whether they were receiving the method procedures or a simulation of the procedures that has no effect. Similarly, the researchers were not aware which couples were receiving the method and which were receiving the simulation until the end of the study. Choose the correct answer below.

The study is a double-blind experiment, and it has a control group and a treatment group.

A company hires independent university scientists to determine whether its​ new, genetically engineered soybean poses any threat to the environment. Are there sources of bias in this​ situation?

There does appear to be sources of bias. The university scientists receive payment from the​ company, so they might be inclined to please the company in the hope of getting projects in the future. ​ Thus, there may be an inclination to provide favorable results.

A researcher plans to investigate the belief that people are more comfortable in the summer sun when they wear clothing with light colors instead of clothing with dark colors. Does it make sense to use a​ double-blind experiment in this​ case?

Yes, because the color of clothing a subject is wearing may have a psychological effect on how comfortable they feel in the sun. It could also influence how the researcher interacts with the subject.

Experimental Study

a study in which we manipulate 1 variable & measure a response in another.

Observational Study

a study in which we merely measure & observe; we do not attempt to manipulate any variables.

A political scientist randomly selects 33 of the 202 representatives currently serving in the legislative body of a​ government, then finds their political party affiliations. Identify the population.

all 202 representatives in the legislative body

In a test of the effectiveness of garlic for lowering​ cholesterol, 59 adults were treated with garlic in a processed tablet form. Cholesterol levels were measured before and after the treatment. The changes in their levels of LDL cholesterol​ (in mg/dL) have an average​ (mean) of 4.9. Identify the population in the given study. Choose the correct answer below.

all adults

Simple Random Sampling

every possible sample of the same sample size is equally likely to be chosen in the sample.

In testing the effectiveness of a new​ vaccine, suppose that researchers used males for the treatment group and females for the placebo group. What is​ confounding?

mixing of effects from different factors so that the effects from the specific factors being studied cannot be determined.

A statistic

number that describes a sample

In a test of the effectiveness of garlic for lowering​ cholesterol, 59 adults were treated with garlic in a processed tablet form. Cholesterol levels were measured before and after the treatment. The changes in their levels of LDL cholesterol​ (in mg/dL) have an average​ (mean) of 4.9. Identify the sample in the given study. Choose the correct answer below.

the 59 adults in the study

In a test of the effectiveness of garlic for lowering​ cholesterol, 59 adults were treated with garlic in a processed tablet form. Cholesterol levels were measured before and after the treatment. The changes in their levels of LDL cholesterol​ (in mg/dL) have an average​ (mean) of 4.9. Identify the population parameter in the given study. Choose the correct answer below.

the average change in the levels of LDL cholesterol​ (in mg/dL) of all teenagers after receiving the garlic treatment

In a test of the effectiveness of garlic for lowering​ cholesterol, 59 adults were treated with garlic in a processed tablet form. Cholesterol levels were measured before and after the treatment. The changes in their levels of LDL cholesterol​ (in mg/dL) have an average​ (mean) of 4.9. Identify the sample statistic in the given study. Choose the correct answer below.

the average change in the levels of LDL cholesterol​ (in mg/dL), 4.9​, of the adults in the study after receiving the garlic treatment

Systematic Sampling

we choose every nth individual in some predetermined fashion to be a part of the sample.