Elementary Statistics

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

cluster sample

What is a closed​ question? What is an open​ question?

A closed question has fixed choices for​ answers, whereas an open question is a​ free-response question.

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

A designed experiment

What is a frame?

A list of the individuals in the population we are studying

Suppose you assigned 40 subjects to each of the three treatment groups. In​ addition, you decided to control the variable exercise by having each subject perform 150 minutes of cardiovascular exercise each week by walking on a treadmill.​ However, the 40 subjects in the placebo group decided they did not want to walk on the treadmill and skipped the weekly exercise. Explain how exercise is now a confounding variable.

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.

What is a designed​ experiment? A. A designed experiment measures the value of the response variable without attempting to influence the value of either the response or explanatory variables. B. 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. C. A designed experiment is a list of all individuals in a population along with certain characteristics of each individual.

B

What is an observational​ study? A. An observational study is a list of all individuals in a population along with certain characteristics of each individual. B. An observational study 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. C. An observational study measures the value of the response variable without attempting to influence the value of either the response or explanatory variables.

C

To determine customer opinion of their safety features​, Daimler-Chrysler randomly selects 80 service centers during a certain week and surveys all customers visiting the service centers. What type of sampling is used?

Cluster

Researchers wanted to test the effectiveness of a new drug therapy for treating patients with manic depression. To do this, they identified 90 patients with a diagnosis of manic depression. 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 manic depression. 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 manic depression. What type of experimental design is​ this? What is the population being​ studied? What is the response variable in this​ study? What is the​ treatment(s)? Identify the experimental units.

Completely randomized design; All patients with a diagnosis of manic depression; The score on the standardized rating scale for manic depression; The new drug therapy, the older drug​ therapy, and placebo therapy; The 90 patients with a diagnosis of manic depression

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? Explain how you would use blinding in this experiment. What is the​ factor? Is it qualitative or​ quantitative? Explain how to use randomization in this experiment. How does randomization neutralize those variables that are not​ controlled?

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. 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.

A television station asks its viewers to call in their opinion regarding the desirability of programs in high definition TV. What type of sampling is​ used?

Convenience

What is meant by confounding?

It exists in a study when the effects of two or more explanatory variables are not separated. So any relation that appears to exist between a certain explanatory variable and the response variable may be due to some other variable not accounted for in the study

To help assess student learning in her music theory courses, a music professor at a community college implemented pre- and​ post-tests for her music theory students. A​ knowledge-gained score was obtained by taking the difference between the two test scores. What type of experimental design is​ this? What is the response variable in this​ experiment? What is the​ treatment?

Matched pair; Difference in test scores; Music theory course

Suppose you are interested in comparing brand A exterior latex paint to brand B exterior latex paint. Design an experiment to determine which paint is better for painting siding.

Matched-pairs design because experimental units are paired up and there are only two levels of treatment.

The survey has a bias. A polling organization conducts a study to estimate the percentage of households that have both parents sharing equally in household chores. It mails a questionnaire to 1786 randomly selected households across the country and asks the head of each household if he or she has both parents sharing equally in household chores. Of the 1786 households selected, 26 responded. ​What best describes the bias in the​ survey?

Non response bias; The polling organization should try contacting households that do not respond by phone or​ face-to-face.

Distinguish between nonsampling error and sampling error.

Nonsampling error is the error that results from the process of obtaining the data.​ Undercoverage, nonresponse​ bias, response​ bias, or​ data-entry errors are all types of nonsampling errors. Sampling error is the error that results because a sample is being used to estimate information about a population. This type of error occurs because a sample gives incomplete information about a population.

What is a lurking variable?

Not accounted for in the study but affects the value of the response variable

What does it mean when sampling is done without replacement?

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

What is replication in an experiment?

Replication is the process of assigning several experimental units to each treatment. It helps to show that observed effects are not due to some characteristic of a single experimental​ unit, but instead are due to the treatment.

The survey has a bias. An abortion rights advocate wants to estimate the percentage of people who favor opening abortion clinics. She conducts a nationwide survey of 1950 randomly selected adults 18 years and older. The interviewer asks the​ respondents, ​"Do you favor supporting women's rights by keeping abortion clinics open question mark ​" What best describes the bias in the​ survey? How can the bias be​ remedied?

Response bias; The interviewer should reword the question.

The manager of a shopping mall wishes to expand the number of shops available in the food court. She has a market researcher survey the first 100 customers who come into the food court during weekend mornings to determine what types of food the shoppers would like to see added to the food court. ​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? What is the best way to remedy this​ problem?

Sampling Bias; Ask customers throughout the day on both weekdays and weekends.

Apple wants to administer a satisfaction survey to its current customers. Using their customer​ database, the company randomly selects 80 customers and asks them about their level of satisfaction with the company. What type of sampling is​ used?

Simple random

Discuss the advantages and disadvantages of each type of question (closed/open).

Since closed questions limit the possible​ responses, they are easier to analyze. Open questions are harder to analyze due to the variety of answers and the chance of misinterpreting an answer.

To determine her blood sugar level​, Charlotte divides up her day into three​ parts: morning,​ afternoon, and evening. She then measures her blood sugar level at 2 randomly selected times during each part of the day. What type of sampling is​ used?

Stratified

To estimate the percentage of defects in a recent manufacturing​ batch, a quality control manager at Daimler-Chrysler selects every 19th van that comes off the assembly line starting with the second until she obtains a sample of 110 vans. What type of sampling is​ used?

Systematic

Determine whether the following statement is true or false. ​Generally, the goal of an experiment is to determine the effect that the treatment will have on the response variable.

The statement is true because an experiment is defined as a controlled study conducted to determine the effect varying one or more factors has on a response​ variable, and any combination of the values of the factors is called a treatment.​ Therefore, the goal of an experiment is to determine the effect that the treatment will have on the response variable.

Determine whether the study depicts an observational study or an experiment. Seventh-grade students are randomly divided into two groups. One 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 its proficiency with that of the other group.

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 lung capacity and proximity to coal mines. A sample of 100 people living within 1 mile of a coal mine is collected and their lung capacity measured. 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.

You wonder whether green tea lowers cholesterol. 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.

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

When a part of the population is proportionally smaller in a sample than in its​ population, this part of the population has been​ under-represented. This could be caused by many different types of​ bias, or even by random chance.

obtained by dividing the population into homogeneous groups and randomly selecting individuals from each group.

stratified sample

What sampling method does not require a frame?

systematic