MAT110 Ch.1

Determine whether the statement is true or false. If it is​ false, rewrite it as a true statement. A statistic is a measure that describes a population characteristic. A. False. A statistic is the science of​ collecting, organizing,​ analyzing, and interpreting data in order to make decisions. B. False. A statistic is a measure that describes a sample characteristic. C. True.

False. A statistic is a measure that describes a sample characteristic.

Determine if the survey question is biased. If the question is​ biased, suggest a better wording. How often do you eat vegetables during an average month​?

No, because it does not lead the respondent to any particular answer.

Determine whether the underlined value is a parameter or a statistic. The average score for a class of 28 students taking a calculus midterm exam was 72%.

Parameter

What is replication in an​ experiment? Why is replication​ important?

Replication is repetition of an experiment under the same or similar conditions. Replication is important because it enhances the validity of the results.

What are the two main branches of​ statistics?

The two main branches of statistics are descriptive statistics and inferential statistics.

What is the level of measurement for ​"Temperature​"?

interval

What is the level of measurement for ​"Year of birth​"?

interval

What is the level of measurement for ​"Allergies​"?

nominal

What is the level of measurement for ​"Marital status​"?

nominal

What is the level of measurement for ​"Change in health (scale of −5 to 5)​"?

ordinal

What is the level of measurement for ​"Pain level (scale of 0 to 10)​"?

ordinal

What is the difference between a census and a​ sampling?

A census includes the entire population. A sampling includes only part of the population.

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

A parameter is a numerical description of a population characteristic. A statistic is a numerical description of a sample characteristic.

How is a sample related to a​ population?

A sample is a subset of a population.

A​ quality-control manager randomly selects 70 bottles of mustard that were filled on August 27 to assess the calibration of the filling machine. What is the population in the​ study? A. All bottles of mustard produced in the plant on August 27. B. The 70 bottles of mustard selected in the plant on August 27. C. The 70 bottles of mustard selected in the plant. D. All bottles of mustard produced in the plant in the given year.

A. All bottles of mustard produced in the plant on August 27.

Select three examples of data sets that have inherent zeros A. Average age of college students in years B. A​ student's level of happiness measured from 0 to 10 C. Temperature in degrees Fahrenheit D. Average monthly precipitation in inches E. Maximum wind speed during a hurricane F. Average IQ score of a high school class

A. Average age of college students in years D. Average monthly precipitation in inches E. Maximum wind speed during a hurricane

Determine whether the statement is true or false. If it is​ false, rewrite it as a true statement. Data at the ordinal level are quantitative only. A. False. Data at the ordinal level can be qualitative or quantitative. B. False. Data at the ordinal level are qualitative only. C. True.

A. False. Data at the ordinal level can be qualitative or quantitative.

A​ quality-control manager randomly selects 70 bottles of mustard that were filled on August 27 to assess the calibration of the filling machine. What is the sample in the​ study? A. The 70 bottles of mustard selected in the plant on August 27. B. All bottles of mustard produced in the plant on August 27. C. All bottles of mustard produced in the plant in the given year. D. The 70 bottles of mustard selected in the plant in August.

A. The 70 bottles of mustard selected in the plant on August 27.

A survey of 12,075 women in a particular country found that 47.6​% received an influenza vaccine for a recent flu season. Identify the sample. A. The immunization status of the 12,075 women selected B. The immunization status of all women in the country C. All women in the country D. The 12,075 women selected

A. The immunization status of the 12,075 women selected

Determine whether the underlined number describes a population parameter or a sample statistic. Explain your reasoning. A survey of 2216 adults in a country found that 82% think that militant terrorists are a major threat to the​ well-being of their country. A. The number is a sample statistic because it describes the people in a​ sample, which is a subset of all of the people in the country. B. The number is a sample statistic because it is a numerical description of all of the people in the country. C. The number is a population parameter because it is a numerical description of all of the people in the country. D. The number is a population parameter because it describes the people in a​ sample, which is a subset of all of the people in the country.

A. The number is a sample statistic because it describes the people in a​ sample, which is a subset of all of the people in the country.

Determine whether the following statement is true or false. If it is​ false, rewrite it as a true statement. Data at the ratio level cannot be put in order. A. The statement is false. A true statement is​ "Data at the ratio level can be placed in a meaningful​ order." B. The statement is false. A true statement is​ "Data at the ratio level can be​ ordered, although it is impossible to determine if one data value is a multiple of​ another." C. The statement is false. A true statement is​ "Data at the ratio level can be​ ordered, although it is impossible to subtract data​ values." D. The statement is true.

A. The statement is false. A true statement is​ "Data at the ratio level can be placed in a meaningful​ order."

Identify the sampling techniques​ used, and discuss potential sources of bias​ (if any). Explain. Assume the population of interest is the student body at a university. Questioning students as they leave a university library​, a researcher asks 368 students about their dating habits.

Convenience sampling is​ used, because students are chosen due to convenience of location. The sample only consists of members of the population that are easy to get. These members may not be representative of the population. Because of the personal nature of the​ question, students may not answer honestly.

Suppose a survey of 952 major-appliance shoppers found that more than 25​% bought extended warranties. Which part of the survey represents the descriptive branch of​ statistics? Make an inference based on the results of the survey. Choose the best inference from the given information. A. There is no association between major-appliance shoppers and buying extended warranties. B. 952 major-appliance shopperswere surveyed. C. 25​% of major-appliance shoppers in the sample bought extended warranties. D. Most major-appliance shoppers do not buy extended warranties.

D. Most major-appliance shoppers do not buy extended warranties.

Determine whether the variable is qualitative or quantitative. Explain your reasoning. Number of brothers A. The variable is qualitative because a number describes an attribute or characteristic. B. The variable is qualitative because a number is found by measuring or counting. C. The variable is quantitative because a number describes an attribute or characteristic. D. The variable is quantitative because a number is found by measuring

D. The variable is quantitative because a number is found by measuring

Determine whether the data set is a population or a sample. Explain your reasoning. The temperature in four state capitals out of 50. A. ​Sample, because it is a collection of temperatures for all of the state capitals, but there are other countries. B. ​Population, because it is a subset of all state capitals. C. ​Population, because it is a collection of temperatures for all of the state capitals. D. ​Sample, because the collection of temperatures for four state capitals is a subset of all state capitals.

D. ​Sample, because the collection of temperatures for four state capitals is a subset of all state capitals.

Use the row of numbers shown below to generate 12 random numbers between 01 and 99. 31075 04957 36044 24197 21935 10848 77061

31, 7, 50, 49, 57, 36, 4, 42, 41, 97, 21, 93

Suppose a survey of 503 women in the United States found that more than 69​% are the primary investor in their household. Which part of the survey represents the descriptive branch of​ statistics? Make an inference based on the results of the survey. Choose the best statement of the descriptive statistic in the problem. Choose the best inference from the given information. A. There is an association between U.S. women and being the primary investor in their household. B. 69​% of women in the sample are the primary investor in their household. C. There is an association between the 503 women and being the primary investor in their household. D. 503 women were surveyed.

A. There is an association between U.S. women and being the primary investor in their household.

Suppose a survey of 503 women in the United States found that more than 69​% are the primary investor in their household. Which part of the survey represents the descriptive branch of​ statistics? Make an inference based on the results of the survey. Choose the best statement of the descriptive statistic in the problem. A. There is an association between U.S. women and being the primary investor in their household. B. 69​% of women in the sample are the primary investor in their household. C. There is an association between the 503 women and being the primary investor in their household. D. 503 women were surveyed.

B. 69​% of women in the sample are the primary investor in their household.

Select three examples of data sets that do not have inherent zeros below. A. Average age of college students in years B. A​ student's level of happiness measured from 0 to 10 C. Temperature in degrees Fahrenheit D. Average monthly precipitation in inches E. Maximum wind speed during a hurricane F. Average IQ score of a high school class

B. A​ student's level of happiness measured from 0 to 10 C. Temperature in degrees Fahrenheit F. Average IQ score of a high school class

A survey of 12,075 women in a particular country found that 47.6​% received an influenza vaccine for a recent flu season. Identify the population A. All women in the country B. The collection of immunization statuses of all women in the country C. The collection of immunization statuses of the 12,075 women selected D. The 12,075 women selected

B. The collection of immunization statuses of all women in the country

Determine whether the following statement is true or false. If it is​ false, rewrite it as a true statement. For data at the interval​ level, you cannot calculate meaningful differences between data entries. A. The statment is false. A true statement is​ "For data at the interval​ level, you cannot calculate meaningful differences between data​ entries." B. The statement is false. A true statement is​ "For data at the interval​ level, you can calculate meaningful differences between data​ entries." C. The statement is false. A true statement is​ "For data at the interval​ level, you​ can't order​ them, but you can calculate meaningful differences between data​ entries." D. The statement is true.

B. The statement is false. A true statement is​ "For data at the interval​ level, you can calculate meaningful differences between data​ entries."

Determine whether the data set is a population or a sample. Explain your reasoning. The salary of teach teacher in a school. A. ​Sample, because it is a collection of salaries for some teachers in the school. B. ​Population, because it is a collection of salaries for all teachers in the school. C. ​Population, because it is a subset of all schools in the city. D. ​Sample, because it is a collection of salaries for all teachers in the school, but

B. ​Population, because it is a collection of salaries for all teachers in the school.

Suppose a survey of 952 major-appliance shoppers found that more than 25​% bought extended warranties. Which part of the survey represents the descriptive branch of​ statistics? Make an inference based on the results of the survey. Choose the best statement of the descriptive statistic in the problem. A. There is no association between major-appliance shoppers and buying extended warranties. B. 952 major-appliance shopperswere surveyed. C. 25​% of major-appliance shoppers in the sample bought extended warranties. D. Most major-appliance shoppers do not buy extended warranties.

C. 25​% of major-appliance shoppers in the sample bought extended warranties.

Determine whether the statement is true or false. If it is​ false, rewrite it as a true statement. More types of calculations can be performed with data at the nominal level than with data at the interval level. A. False. The same types of calculations can be performed with data at the nominal level and with data at the interval level. B. True. C. False. More types of calculations can be performed with data at the interval level than with data at the nominal level.

C. False. More types of calculations can be performed with data at the interval level than with data at the nominal level.

The years that a television show on a particular network won an award for best comedy series are shown below. 1951 1978 1979 1984 1986 1989 2003 2007 2009 Determine the level of measurement of the data set. Explain your reasoning. A. Ratio. The data can be ordered and differences between data entries are​ meaningful, and a zero entry is an inherent zero. B. Nominal. No mathematical computations can be made. C. Interval. The data can be ordered and differences between data entries are​ meaningful, but a zero entry is not an inherent zero. D. Ordinal. The data can be arranged in​ order, or​ ranked, but differences between data entries are not meaningful.

C. Interval. The data can be ordered and differences between data entries are​ meaningful, but a zero entry is not an inherent zero.

The list of books that your friend read for school for the past five months is shown below. Gone Girl Spring Fever Threat Vector The Racketeer Private London Identify the level of measurement of the data set. Explain your reasoning. A. Interval. The data can be ordered and differences between data entries are​ meaningful, but the zero entry is not an inherent zero. B. Ratio. The data can be ordered and differences between data entries are​ meaningful, and the zero entry is an inherent zero. C. Nominal. The data are categorized using names, labels, or qualities, but the data cannot be ranked or arranged in order. D. Ordinal. The data can be arranged in order, but the differences between data entries

C. Nominal. The data are categorized using names, labels, or qualities, but the data cannot be ranked or arranged in order.

The jersey numbers for players on a soccer team are listed below. 15, 5, 58, 14, 9, 11, 19, 10, 27, 21, 13, 24, 18, 17, 16, 7, 1, 22, 12, 37, 40, 30, 33, 35, 6, 88, 28 Identify the level of measurement of the data set. Explain your reasoning. A. Ordinal. The data can be arranged in​ order, or​ ranked, but differences between data entries are not meaningful. B. Ratio. The data can be ordered and differences between data entries are​ meaningful, and the zero entry is an inherent zero. C. Nominal. The data are categorized using​ numbers, but no mathematical computations can be made. D. Interval. The data can be ordered and differences between data entries are​ meaningful, but the zero entry is not an inherent zero.

C. Nominal. The data are categorized using​ numbers, but no mathematical computations can be made.

Name each level of measurement for which data can be qualitative. A. Interval B. Ratio C. Ordinal D. Nominal

C. Ordinal D. Nominal

Determine whether the following statement is true or false. If it is​ false, rewrite it as a true statement. A sample statistic will not change from sample to sample. A. The statement is true. B. The statement is false. A sample parameter will not change from sample to sample. C. The statement is false. A sample statistic can change from sample to sample. D. The statement is false. A population statistic will not change from population to population.

C. The statement is false. A sample statistic can change from sample to sample.

What is the difference between an observational study and an​ experiment?

In an​ experiment, a treatment is applied to part of a population and responses are observed. In an observational​ study, a researcher measures characteristics of interest of a part of a population but does not change existing conditions.

Why is a sample used more often than a​ population?

It is usually impossible to count the entire population.

Identify the sampling techniques​ used, and discuss potential sources of bias​ (if any). Explain. In​ 1965, researchers used random digit dialing to call 800 people and ask what obstacles kept them from saving for retirement. What type of sampling was​ used?

Simple random sampling was​ used, since each number had an equal chance of being​ dialed, so all samples of 800 phone numbers had an equal chance of being selected. Individuals may have refused to participate in the sample. This may have made the sample less representative of the population. Telephone sampling only includes people who had telephones. People who owned telephones may have been older or wealthier on​ average, and may not have been representative of the entire population. Individuals may have not been available when the researchers were calling. Those individuals that were available may have not been representative of the population.

Identify the sampling techniques​ used, and discuss potential sources of bias​ (if any). Explain. Lettuce is planted on a 46​-acre field. The field is divided into​ one-acre subplots. A sample is taken from each subplot to estimate the harvest.

Stratified sampling is​ used, since the field is divided into subplots and a random sample is taken from each subplot. Certain subplots may have more or fewer lettuce plants than others. Samples from these subplots may bias the overall sample.

A pharmaceutical company wants to test the effectiveness of a new allergy drug. The company identifies 250 females​ 30-35 years old who suffer from severe allergies. The subjects are randomly assigned into two groups. One group is given the new allergy drug and the other is given a placebo that looks exactly like the new allergy drug. After six​ months, the​ subjects' symptoms are studied and compared. Identify the experimental units and treatments used in this experiment.

The experimental units are the​ 30- to​ 35-year-old females being given the treatment. The treatment is the new allergy drug.

Determine if the survey question is biased. If the question is​ biased, suggest a better wording. Why is eating eggs good for​ you?

The question is biased. The wording​ "How do you think eating eggs affects your​ health?" would be better.

A pharmaceutical company wants to test the effectiveness of a new allergy drug. The company identifies 250 females​ 30-35 years old who suffer from severe allergies. The subjects are randomly assigned into two groups. One group is given the new allergy drug and the other is given a placebo that looks exactly like the new allergy drug. After six​ months, the​ subjects' symptoms are studied and compared. How could this experiment be designed to be a​ double-blind?

The study would be a​ double-blind study if both the researcher and the patient did not know which patient received the real drug or the placebo.

Determine whether you would take a census or use a sampling to collect data for the study described below. If you would use a​ sampling, determine which sampling technique you would use. Explain. The average credit card debt of the 60 employees of a company.

The study is a census​, because the population is small enough for it to be practical to record all of the responses.

Determine whether the study is an observational study or an experiment. Explain. In a survey of 1220 adults in a​ country, 52​% said the​ country's leader should release all medical information that might affect their ability to serve.

The study is observational, because it does not apply a treatment to the adults.

A pharmaceutical company wants to test the effectiveness of a new allergy drug. The company identifies 250 females​ 30-35 years old who suffer from severe allergies. The subjects are randomly assigned into two groups. One group is given the new allergy drug and the other is given a placebo that looks exactly like the new allergy drug. After six​ months, the​ subjects' symptoms are studied and compared. Identify a potential problem with the experiment design being used and suggest a way to improve it.

There may be a bias on the part of the researcher if the researcher knows which patients were given the real drug.

What is the level of measurement for ​"Time since last visit​"?

ratio

What is the level of measurement for ​"Weight​"?

ratio