Module 0 Homework

Do people walk faster in an airport when they are departing​ (getting on a​ plane) or after they have arrived​ (getting off a​ plane)? An interested passenger watched a random sample of people departing and a random sample of people arriving and measured the walking speed​ (in feet per​ minute) of each. What type of study design is being​ performed?

Observational study

A variable is at the​ _______ level of measurement if it allows for the values of the variable to be arranged in a specific order but the differences between values either cannot be determined or are meaningless.

Ordinal

Suppose a pharmaceutical company is designing a​ double-blind experiment to test their new allergy medication. They divide the 200 subjects by gender and then randomly assign the men and women to either receive the medication or a placebo. The researcher finds that even the group receiving the placebo​ (a sugar​ pill) showed a decrease in allergy symptoms. Which of the following accounts for this​ result?

Placebo effect

A company tracked all credit card purchases during the year 2005 and measured two​ variables: (1) the type of credit card used (VISA, MasterCard, or American Express), (2) the amount (in dollars) of the monthly minimum payment. Does the data set collected represent a population or a sample?

Population

The​ _________________ is/are the entire group of individuals or items being studied.

Population

A study examined the appreciation effect of getting a gift for a significant other. In the​ study, the researchers investigated the link between engagement ring price and level of appreciation of the recipient (measured on a 6​-point scale where 1=​"not at all​" and 6=​"to a great extent​"). Participants for the study were those who used a popular Web site for engaged couples. Of the​ respondents, those who paid really high or really low prices were​ excluded, leaving a sample size of 38 respondents. Define the variables measured and classify them as quantitative or qualitative.

Price, quantitative; Appreciation level, qualitative

Is profession qualitative or​ quantitative? Why?

Profession is a qualitative variable. Its values are not numerical.

A company tracked all credit card purchases during the year 2005 and measured two​ variables: (1) the type of credit card used (VISA, MasterCard, or American Express), (2) the amount (in dollars) of the monthly minimum payment. Identify the type​ (quantitative or​ qualitative) of each variable measured. Is the variable​ (1) qualitative or​ quantitative?

Qualitative

A​ ________________ variable classifies individuals based on some attribute or characteristic.

Qualitative

Is native language qualitative or quantitative?

Qualitative

Is natural hair color qualitative or​ quantitative?

Qualitative

Suppose​ you're given a data set that classifies each sample unit into one of four​ categories: A,​ B, C, or D. You plan to create a computer database consisting of these​ data, and you decide to code the data as A=​1, B=​2, C=​3, and D=4. Are the data consisting of the classifications​ A, B,​ C, and D qualitiative or​ quantitative? After the data are input as​ 1, 2,​ 3, or​ 4, are they qualitative or​ quantitative? Are the data consisting of the classifications​ A, B,​ C, and D qualitiative or​ quantitative?

Qualitative, because they can only be classified into categories.

Suppose​ you're given a data set that classifies each sample unit into one of four​ categories: A,​ B, C, or D. You plan to create a computer database consisting of these​ data, and you decide to code the data as A=​1, B=​2, C=​3, and D=4. Are the data consisting of the classifications​ A, B,​ C, and D qualitiative or​ quantitative? After the data are input as​ 1, 2,​ 3, or​ 4, are they qualitative or​ quantitative? After the data are input as​ 1, 2,​ 3, or​ 4, are they qualitative or​ quantitative?

Qualitative, because they cannot be meaningfully​ added, subtracted,​ multiplied, or divided.

A company tracked all credit card purchases during the year 2005 and measured two​ variables: (1) the type of credit card used (VISA, MasterCard, or American Express), (2) the amount (in dollars) of the monthly minimum payment. Identify the type​ (quantitative or​ qualitative) of each variable measured. Is the variable​ (2) qualitative or​ quantitative?

Quantitative

A​ ________________ variable counts or measures something and has numeric values.

Quantitative

Is size of home qualitative or quantitative?

Quantitative

Is time worked in a week qualitative or quantitative?

Quantitative

Explain the difference between qualitative and quantitative data.

Quantitative data are numerical in​ nature, while qualitative data are categorical in nature.

A study examined the appreciation effect of getting a gift for a significant other. In the​ study, the researchers investigated the link between engagement ring price and level of appreciation of the recipient (measured on a 6​-point scale where 1=​"not at all​" and 6=​"to a great extent​"). Participants for the study were those who used a popular website for engaged couples. Of the​ respondents, those who paid really high or really low prices were​ excluded, leaving a sample size of 38 respondents. Identify the experimental units for this study.

Recently married couples who used a particular website

A study examined the appreciation effect of getting a gift for a significant other. In the​ study, the researchers investigated the link between engagement ring price and level of appreciation of the recipient (measured on a 6​-point scale where 1=​"not at all​" and 6=​"to a great extent​"). Participants for the study were those who used a popular Web site for engaged couples. Of the​ respondents, those who paid really high or really low prices were​ excluded, leaving a sample size of 38 respondents. Do the data represent a population or a​ sample?

The data represent a sample since the data are a subset of units.

Which of the following is not true about the process of​ statistics? A. If data are not collected​ properly, the conclusions that are drawn will be meaningless. B. The first step in the process of statistics is to collect the data. Your answer is correct. C. When the results from a sample are extended to the​ population, it is called inference. D. Data are typically collected from a sample because it is too difficult and expensive to collect data from an entire population.

The first step in the process of statistics is to collect the data.

Is time worked in a week qualitative or quantitative? Why?

Time worked in a week is a quantitative variable. Its values are numerical.

Can a qualitative variable have values that are​ numeric? Why or why​ not?

Yes; it is possible to have numeric variables that do not count or measure​ anything, and, as a​ result, are qualitative rather than quantitative.

A medical study was investigating if getting a flu shot actually reduced the risk of developing the flu. From a group of adult​ volunteers, researchers randomly assigned half to receive an injection that contained the drug believed to reduce the risk of getting the flu and the other half to receive an injection containing no active ingredient​ (i.e. sugar​ water). What type of study is being​ performed?

Completely randomized experimental design

Elmo likes music. He wondered if listening to music while studying will improve scores on an exam. Fifty students who were to take the midterm in a week agreed to be part of a study. Half were randomly assigned to listen to classical music while studying for the exam. The other half were told not to listen to any music while studying for the exam. What type of study is being​ performed?

Completely randomized experimental design

If the effect of two factors on the response variable cannot be​ distinguished, what can be concluded about the​ experiment?

Confounding has occurred in the experiment.

Suppose every student in a class is surveyed and it is reported that​ 75% of the class plans to take another math class. Is this an example of descriptive or inferential​ statistics? Explain.

Descriptive​ statistics; The results of the class sample are described without making any generalizations about the population of all students at the school.

Is gender qualitative or​ quantitative? Why?

Gender is a qualitative variable. Its values are not numerical.

Is lucky day of the week qualitative or​ quantitative? Why?

Lucky day of the week is a qualitative variable. Its values are not numerical.

Is natural hair color qualitative or​ quantitative? Why?

Natural hair color is a qualitative variable. Its values are not numerical.

A variable is at the​ _______ level of measurement if the values of the variable​ name, label, or categorize.

Nominal

A qualitative variable can be at which levels of​ measurement?

Nominal or ordinal

Is number of pets in a family qualitative or quantitative? Why?

Number of pets in a family is a quantitative variable. Its values are numerical.

Is number of brothers and sisters qualitative or quantitative? Why?

Numbers of brothers and sisters is a quantitative variable. Its values are numerical.

What is a placebo and what purpose does it serve in an​ experiment?

A placebo is a fake treatment that looks like the treatment being tested in the experiment. Placebos blind subjects so they do not know whether or not they are receiving the treatment.

Explain how populations and samples differ.

A population is a set of units of interest to a study. A sample is a subset of the units of a population.

What is a representative​ sample? What is its​ value?

A representative sample is a sample that exhibits characteristics typical of those possessed by the population of interest. It is valuable because these characteristics allow inferential statistics to be applied.

Explain why Social Security Number is considered a qualitative variable even though it contains numbers.

Addition and subtraction of Social Security Numbers does not provide meaningful results. This makes it qualitative even though it is numeric.

A medical study was investigating if getting a flu shot actually reduced the risk of developing the flu. From a group of adult​ volunteers, researchers randomly assigned half to receive an injection that contained the drug believed to reduce the risk of getting the flu and the other half to receive an injection containing no active ingredient​ (i.e. sugar​ water). Because the control group received a​ placebo, what type of study was​ performed?

Blinded

An article in a reputable journal discussed several data collection methods for testing the efficacy of a new program designed to reduce​ drug-related crimes in a city. The sample consisted of 56​ "hot spots"—areas of the city with a high crime rate but not necessarily a high drug crime rate. In Method​ 1, the new program will be implemented in half of the 56 hot spots​ (selected at​ random); the other half will not implement the program​ (the "no​ treatment" group). In Method​ 2, the 56 hot spots will be divided into four groups based on the level of drug crimes—very high drug crime rate​ (10 hot​ spots), high rate​ (8 hot​ spots), moderate rate​ (26 hot​ spots), and low rate​ (12 hot​ spots). In each​ group, half the hot spots will be randomly assigned the new crime prevention program and the other half no treatment. For both​ methods, after several weeks the crime rates in the hot spots where the program was implemented will be compared with those with no treatment. Identify the data collection method for Method 1.

Designed experiment

An article in a reputable journal discussed several data collection methods for testing the efficacy of a new program designed to reduce​ drug-related crimes in a city. The sample consisted of 56​ "hot spots"—areas of the city with a high crime rate but not necessarily a high drug crime rate. In Method​ 1, the new program will be implemented in half of the 56 hot spots​ (selected at​ random); the other half will not implement the program​ (the "no​ treatment" group). In Method​ 2, the 56 hot spots will be divided into four groups based on the level of drug crimes—very high drug crime rate​ (10 hot​ spots), high rate​ (8 hot​ spots), moderate rate​ (26 hot​ spots), and low rate​ (12 hot​ spots). In each​ group, half the hot spots will be randomly assigned the new crime prevention program and the other half no treatment. For both​ methods, after several weeks the crime rates in the hot spots where the program was implemented will be compared with those with no treatment. Identify the data collection method for Method 2.

Designed experiment

Explain why city altitude is a variable at the interval and not ratio level of measurement.

Differences in altitudes can be found and are meaningful.​ However, there is no natural zero starting point since sea level varies over geological time scales.

In a television​ advertisement, a company called​ "Waist Away" claimed the workout program on their set of DVDs would help people lose weight more than any other DVD workout program. To test this​ claim, an independent​ company, called​ "Slim Down," selected one other DVD program. They then randomly assigned half the volunteers to the Waist Away program and the other half to the Slim Down program. Each participant was weighed before they started the program and then regularly participated in their assigned program for one month. After one​ month, each participant was weighed again. The percent of weight lost was recorded for each​ person, where negative values indicated a weight gain. What type of study was​ performed?

Experiment

Suppose every student in a class is surveyed and it is found that​ 75% of the class plans to take another math class. It is reported that​ 75% of all students at the school plan to take another math class. Is this an example of descriptive or inferential​ statistics? Explain.

Inferential​ statistics; the results of the class sample are extended to make a generalization about the population of all students at the school.

An article in a reputable journal discussed several data collection methods for testing the efficacy of a new program designed to reduce​ drug-related crimes in a city. The sample consisted of 56​ "hot spots"—areas of the city with a high crime rate but not necessarily a high drug crime rate. In Method​ 1, the new program will be implemented in half of the 56 hot spots​ (selected at​ random); the other half will not implement the program​ (the "no​ treatment" group). In Method​ 2, the 56 hot spots will be divided into four groups based on the level of drug crimes—very high drug crime rate​ (10 hot​ spots), high rate​ (8 hot​ spots), moderate rate​ (26 hot​ spots), and low rate​ (12 hot​ spots). In each​ group, half the hot spots will be randomly assigned the new crime prevention program and the other half no treatment. For both​ methods, after several weeks the crime rates in the hot spots where the program was implemented will be compared with those with no treatment. Is this an application of descriptive or inferential​ statistics? Explain.

It is an application of inferential statistics because it utilizes sample data to make a generalization about a larger set of​ data, drug crime rate.

What is​ statistics?

It is the science that deals with​ collection, classification,​ analysis, and interpretation of information or data.

An article in a reputable journal discussed several data collection methods for testing the efficacy of a new program designed to reduce​ drug-related crimes in a city. The sample consisted of 56​ "hot spots"—areas of the city with a high crime rate but not necessarily a high drug crime rate. In Method​ 1, the new program will be implemented in half of the 56 hot spots​ (selected at​ random); the other half will not implement the program​ (the "no​ treatment" group). In Method​ 2, the 56 hot spots will be divided into four groups based on the level of drug crimes—very high drug crime rate​ (10 hot​ spots), high rate​ (8 hot​ spots), moderate rate​ (26 hot​ spots), and low rate​ (12 hot​ spots). In each​ group, half the hot spots will be randomly assigned the new crime prevention program and the other half no treatment. For both​ methods, after several weeks the crime rates in the hot spots where the program was implemented will be compared with those with no treatment. Given that there is a great deal of variation in the drug crime rates at the 56 hot​ spots, which data collection method do you​ recommend? Explain.

Recommend Method 2 since it divides the hot spots based on the level of drug crimes.

A sample is said to be ​ __________ if the statistics computed from it accurately reflect the corresponding population parameters.

Representative

The​ _________________ is/are a subset of the population that is being studied.

Sample

Suppose that a researcher is interested in the average standardized test score for fifth graders in a local school district. The fifth graders at a specific school would comprise a​ ___________ and their average test score would be a​ ___________.

Sample; statistic

Is size of home qualitative or​ quantitative? Why?

Size of home is a quantitative variable. Its values are numerical.

A​ _________________ is a numerical measurement describing some characteristic of a sample.

Statistic