MTH245

Determine whether each number describes a population parameter or a sample statistic. Explain. In a recent year, the average evidence-based reading and writing score on the SAT was 543.

(b) Population parameter. The average evidence based reading and writing score of 543 is a numerical description of all test-takers in a recent year.

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

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

What is an inherent​ zero? Describe three examples of data sets that have inherent zeros and three that do not. Select three examples of data sets that have inherent zeros below. --Average age of college students in years --Average IQ score of a high school class --Average monthly precipitation in inches --Maximum wind speed during a hurricane --A​ student's level of happiness measured from 0 to 10 --Temperature in degrees Fahrenheit

--Average age of college students in years --Average monthly precipitation in inches --Maximum wind speed during a hurricane

Suppose a survey of 990 major-appliance shoppers found that more than 30​% bought extended warranties. Which part of the survey represents the descriptive branch of​ statistics? Make an inference based on the results of the survey.

30​% of major-appliance shoppers in the sample bought extended warranties. Most major-appliance shoppers do not buy extended warranties.

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

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

Researchers surveyed 19,183 U.S. physicians, asking for the information below. ★location (region of the U.S.) ★income employment status (private practice or an employee) ★benefits received (health insurance, liability coverage, etc.) ★specialty (cardiology, family medicine, radiology, etc.) ★time spent seeing patients per week (hours) Is the data collected qualitative, quantitative, or both?Explain your reasoning.

Both. Location, employment status, benefits received, and speciality are qualitative because they are attributes. Income and time spent seeing patients per week are quantitative because they are numerical measurements.

Determine whether you would take a census or use a sampling. If you would use a sampling, determine which sampling technique you would use. Explain. (b) The average age of the 30 employees of a company

Census, because the population is small and it is relatively easy to obtain the ages of the 30 employees.

Identify the sampling technique used. At a local community​ college, five statistics classes are randomly selected out of 20 and all of the students from each class are interviewed.

Cluster

Identify the sampling technique used. A community college student interviews everyone in a statistics class to determine the percentage of students that own a car.

Convenience

Identify the sampling technique used, and discuss potential sources of bias (if any). Explain. Questioning teachers as they leave a faculty lounge, a researcher asks 45 of them about their teaching styles.

Convenience sampling is used because a sample is taken from members of a population that are readily available. The sample may be biased because the teachers at that school may not be representative of the population of teachers.

Identify the sampling technique used in each study. Explain your reasoning. (a) A journalist asks people at a campground about air pollution.

Convenience sampling is used because all the people sampled are in one convenient location.

Which technique used in Exercise 7 could lead to a biased study? Explain. Exercise 7） (a) A journalist asks people at a campground about air pollution. (b) For quality assurance, every tenth machine part is selected from an assembly line and measured for accuracy. (c) A study on attitudes about smoking is conducted at a college. The students are divided by class (freshman, sophomore, junior, and senior). Then a random sample is selected from each class and interviewed. 1

Convenience sampling. People at campgrounds may be strongly against air pollution because they are at an outdoor location.

Determine whether the study depicts an observational study or an experiment. A medical researcher obtains a sample of adults suffering from diabetes. She randomly assigns 72 people to a treatment group and 72 to a placebo group. The treatment group receives a medication over a period of three months and the placebo group receives a placebo over the same time frame. At the end of three months the​ patients' symptoms are evaluated.

Experiment

Determine whether the study is an observational study or an experiment. Explain. Researchers conduct a study to determine whether taking a multivitamin daily affects cognitive health among men as they age. To perform the study, researchers studied 5947 male physicians ages 65 years or older and had one group take a multivitamin daily and had another group take a placebo daily.

Experiment. The study applies a treatment (multivitamin) to the subjects.

Determine whether the statement is true or false. More types of calculations can be performed with data at the nominal level than with data at the interval level.

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

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.

In a recent study on the effects of sleep and test​ results, volunteers took a math test. The volunteers who had 8 hours of sleep were three times more likely to answer questions correctly on the math test than were​ sleep-deprived volunteers.

Individuals who are not sleep deprived寝不足 will be more likely to answer math questions correctly than individuals who are sleep deprived.

Identify the data​ set's level of measurement. temperatures of 95 selected refrigerators

Interval

Determine the level of measurement of the data set. Explain your reasoning. The years of birth for the runners in the Boston marathon

Interval, because meaningful differences between years can be calculated, but a zero entry is not an inherent zero.

Identify the data​ set's level of measurement. marriage status​ (married, single, or​ divorced) of the faculty at a university

Nominal

The jersey numbers for players on a football team are listed below. 20--7---67--67--1+

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

Researchers surveyed 19,183 U.S. physicians, asking for the information below. ★location (region of the U.S.) ★income employment status (private practice or an employee) ★benefits received (health insurance, liability coverage, etc.) ★specialty (cardiology, family medicine, radiology, etc.) ★time spent seeing patients per week (hours) Determine the level of measurement for each item above.

Nominal: location, employment status, benefits received, specialty Ratio: income, time spent seeing patients per week

Researchers surveyed 19,183 U.S. physicians, asking for the information below. ★location (region of the U.S.) ★income employment status (private practice or an employee) ★benefits received (health insurance, liability coverage, etc.) ★specialty (cardiology, family medicine, radiology, etc.) ★time spent seeing patients per week (hours) Determine whether the study is an observational study or an experiment. Explain.

Observational study. The study does not attempt to influence the responses of the physicians and there is no treatment.

Determine whether the study is an observational study or an experiment. Explain. Researchers conduct a study to determine whether body mass index (BMI) influences mortality死亡率. To conduct the study, researchers obtained the BMIs of 3,951,455 people.

Observational study. The study does not attempt to influence the responses of the subjects and there is no treatment.

Determine the level of measurement of the data set. Explain your reasoning. The top 10 grossing films released in a year

Ordinal, because data can be arranged in order, but the differences between data entries make no sense.

Determine the level of measurement of the data set. Explain your reasoning. A list of badge numbers of police officers at a precinct

Ordinal, because badge numbers can be ordered and often indicate seniority of service, but no meaningful mathematical computation can be performed.

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

The graph to the right shows the responses to the question, "Will we win the championship?" Identify the level of measurement of the data listed on the horizontal and vertical axes in the figure. Percent 0〜50％ (vertical axis) Response（A〜E）（the horizontal axis） --Identify the level of measurement of the data listed on the horizontal axis --Identify the level of measurement of the data listed on the vertical axis

Percent 0〜50%--Ratio Response（A〜E）--Ordinal

A survey of 120 law firms in a country found that the average hourly billing rate for partners was $564. Identify the population and the sample and describe the data set.

Population All law firm in the country Sample The law firms that were surveyed Data sets The average hourly billing rate for partners of 120 law firms was $564

In a​ poll, 1,003 men in a country were asked whether they favor or oppose the use of​ "federal tax dollars to fund medical research using stem cells obtained from human​ embryos." Among the​ respondents, 48​% said that they were in favor. Identify the population and the sample.

Population All men in the country Sample The 1003 men selected

Determine whether each number describes a population parameter or a sample statistic. Explain your reasoning. At a college, 90% of the members of the Board of Trustees approved the contract of the new president.

Population Parameter. The 90% of members that approved the contract of the new president is a numerical description of all Board of Trustees members.

Researchers surveyed 19,183 U.S. physicians, asking for the information below. ★location (region of the U.S.) ★income employment status (private practice or an employee) ★benefits received (health insurance, liability coverage, etc.) ★specialty (cardiology, family medicine, radiology, etc.) ★time spent seeing patients per week (hours) Identify the population and the sample.

Population: Collection of the responses of all U.S. physicians Sample: Collection of the 19,183 U.S. physicians who were sampled.

Identify the population and the sample in the study. A study of the dietary habits of 359,264 Korean adolescents was conducted to find a link between dietary habits and school performance.

Population: Collection of the school performance of all Korean adolescents Sample: Collection of the school performance of the 359,264 Korean adolescents in the study

Determine whether the data are qualitative or quantitative. Explain. (a) A list of debit card personal identification numbers

Qualitative Because debit card personal identification numbers are labels and it does not make sense to find differences between numbers

Determine whether the variable is qualitative or quantitative. Explain your reasoning. Postal ZIP codes

Qualitative. ZIO codes are attributes or labels.

Determine whether the data are qualitative or quantitative. Explain. (b) The final scores on a video game

Quantitative, because final scores are numerical measurements.

Determine whether the data are qualitative or quantitative, and determine the level of measurement of the data set. Explain your reasoning. The grade point averages (GPAs) for a class of students are listed. 3.6 - 3.2 - 2.0 - 3.8 - 3.0 - 3.5 - 1.7

Quantitative. Interval. The grade point averages are numerical measurements. Data can be ordered and meaningful differences can be calculated, but it does not make sense to say that a person with a 3.8 GPA is twice as smart as a person with a 1.9 GPA.

Determine whether the data are qualitative or quantitative, and determine the level of measurement of the data set. Explain your reasoning. (a) The numbers of employees at fast-food restaurants in a city are listed. 20 - 11 - 6 - 31 - 17 - 23 - 12 - 18 - 40

Quantitative. Ratio. The number of employees are numerical measurements. A ratio of two data values can be formed, so it makes sense to say that 40 employees are twice as many as 20 employees.

Identify the sampling technique used. A lobbyist for a major airspace firm assigns a number to each legislator and then uses a computer to randomly generate ten numbers. The lobbyist contacts the legislators corresponding to these numbers.

Random

Identify the sampling technique used. Based on 11,000 responses from 32,000 questionnaires sent to its​ alumni, a major university estimated that the annual salary of its alumni was ​$117,000 per year.

Random

An experiment is performed to test the effects of a new drug on high blood pressure. The experimenter identifies 320 people ages 35-50 years old with high blood pressure for participation in the experiment. The subjects are divided into equal groups according to age. Within each group, subjects are then randomly selected to be in either the treatment group or the control group. What type of experimental design is being used for this experiment?

Randomized block design

Identify the data​ set's level of measurement. number of milligrams of tar in 34 cigarettes

Ratio

Identify the data​ set's level of measurement. numbers of touchdowns scored by a major university in five randomly selected games 3--5--1--4--4

Ratio

Determine the level of measurement of the data set. Explain your reasoning. The horsepowers of racing car engines

Ratio, because horsepower of one car can be expressed as a multiple of another.

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.

Determine whether each number describes a population parameter or a sample statistic. Explain your reasoning. A survey of 727 small business owners found that 25% reported job openings they could not fill.

Sample statistic. The value 25% is a numerical description of a sample of small business owners.

Determine whether each number describes a population parameter or a sample statistic. Explain. (a) A survey of 1003 U.S. adults ages 18 years and older found that 72% own a smartphone.

Sample statistic. The value of 72% is a numerical description of a sample of U.S. adults ages 18 years and older.

Determine whether each number describes a population parameter or a sample statistic. Explain your reasoning. (a) A survey of 1000 U.S. adults found that 52% think that the introduction of driverless cars will make roads less safe.

Sample statistic. The value 52% is a numerical description of a sample of U.S. adults.

Determine whether you would take a census or use a sampling. If you would use a sampling, determine which sampling technique you would use. Explain. (a) The most popular type of investment among investors in New Jersey

Sampling, because the population of New Jersey is too large for the most popular type of investment to be easily recorded. Random sampling would be advised because it would be easy to select people from New Jersey randomly and then record their most popular type of investment.

Identify the sampling technique used, and discuss potential sources of bias (if any). Explain. Chosen at random, 625 customers at an electronics store are contacted and asked their opinions of the service they received.

Simple random sampling is used because each customer has an equal chance of being contacted, and all samples of 625 customers have an equal chance of being selected

Identify the sampling techniques​ used, and discuss potential sources of bias​ (if any). Explain. In​ 1965, researchers used random digit dialing to call 1100 people and ask what obstacles kept them from attending town hall meetings.

Simple random sampling was​ used, since [each number had an equal chance] of being​ dialed, so all samples of 1100 phone numbers had an [equal chance of being selected.]

Determine whether the underlined numerical value [ ] is a parameter or a statistic. Explain your reasoning. The average annual salary of 50 of a company's 800 employees employee's is [$54000]

Statistic​, because the data set of salaries of 50 employees is a sample.

Identify the sampling technique used. ​Thirty-five sophomores, 27 juniors and 62 seniors are randomly selected from 525 ​sophomores, 232 juniors and 583 seniors at a certain high school.

Stratified

Identify the sampling technique used. A researcher randomly selects and interviews fifty male and fifty female teachers.

Stratified

Identify the sampling technique used, and discuss potential sources of bias (if any). Explain. Chosen at random, 200 male and 200 female high school students are asked about their plans after high school.

Stratified sampling is used because the high school students are divided into strata (male and female), and a sample is selected from each stratum.

Identify the sampling technique used in each study. Explain your reasoning. A study on attitudes about smoking is conducted at a college. The students are divided by class (freshman, sophomore, junior, and senior). Then a random sample is selected from each class and interviewed.

Stratified sampling is used because the population is first stratified and then a sample is collected from each stratum.

Identify the sampling technique used. Every fifth person boarding a plane is searched thoroughly.

Systematic

Identify the sampling technique used in each study. Explain your reasoning. For quality assurance, every tenth machine part is selected from an assembly line and measured for accuracy

Systematic sampling is used because every tenth machine part is sampled.

Use the Venn diagram to identify the population and the sample. ┏━━━━━━━━━━━━ ┃ The ages of car owners in a certain county ┃ ┏━━━━━━━━━━━ ┃ ┃ The age of car owners in the county who work a home ┃ ┗━━━━━━━━━━━ ┗━━━━━━━━━━━━ Choose the correct description of the population. -The ages of car owners in the county -The numbers of car owners in the county

The ages of car owners in the county

Use the Venn diagram to identify the population and the sample. ┏━━━━━━━━━━━━ ┃ The ages of car owners in a certain county ┃ ┏━━━━━━━━━━━ ┃ ┃ The age of car owners in the county who work a home ┃ ┗━━━━━━━━━━━ ┗━━━━━━━━━━━━ Choose the correct description of the sample. -The ages of car owners in the county who work at home -The ages of car owners in the county -The numbers of car owners in the county

The ages of car owners in the county who work at home

A study of 809 senior citizens shows that participants who exercise regularly exhibit less of a decline in cognitive ability than those who barely exercise at all. From this​ study, a researcher infers that your cognitive ability increases the more you exercise. What is wrong with this type of​ reasoning?

The inference may incorrectly imply that exercise increases a​ person's cognitive ability. The study shows a slower decline in cognitive ability.

Determine whether the survey question is biased. If the question is biased, suggest better wording. Do you agree that the town's ban on skateboarding in parks is unfair?

The question is biased because it already suggests that the town's ban on skateboarding in parks is unfair. The question could be written as "What are your thoughts on the town's ban on skateboarding in parks?"

In a recent study on the effects of sleep and test​ results, volunteers took a math test. The volunteers who had 8 hours of sleep were three times more likely to answer questions correctly on the math test than were​ sleep-deprived volunteers. Identify the sample used in the study. What is the​ sample's population?

The sample is the test results of the volunteers in the study. The population is the collection of the test results of all individuals who completed the math test.

Determine whether the following statement is true or false. A placebo is actual treatment.

The statement is false. A placebo is a fake treatment.

Determine whether the following statement is true or false. A​ double-blind experiment is used to increase the placebo effect.

The statement is false. Double blinding is used to decrease the placebo effect.

In a recent study on the effects of sleep and test​ results, volunteers took a math test. The volunteers who had 8 hours of sleep were three times more likely to answer questions correctly on the math test than were​ sleep-deprived volunteers. Which part of the study represents the descriptive branch of​ statistics?

The statement​ "three times more likely to answer questions​ correctly" is an example of descriptive statistics.

Determine whether the survey question is biased. If the question is biased, suggest better wording. (a) How many hours of sleep do you get on a normal night?

The survey question is unbiased.

Determine whether the variable is qualitative or quantitative. Explain your reasoning. Number of brothers

The variable is quantitative because a number is found by measuring or counting.

What is the difference between a random sample and a simple random​ sample?

With a random​ sample, 「each individual 」has the same chance of being selected. With a simple random​ sample, 「all samples of the same size」 have the same chance of being selected.

What are the two main branches of​ statistics? The two main branches of statistics are---

descriptive statistics and inferential statistics.