Chapter 1 HW Questions
What are the two main branches of statistics?
descriptive statistics and inferential statistics
Why is a sample used more often than a population?
it is usually impossible to count the entire population
Name each level of measurement for which data can be quantitative.
ordinal, interval, ratio
Name each level of measurement for which data can be qualitative.
ordinal, nominal
Determine whether the underlined value is a parameter or a statistic. Telephone interviews of 1502 adults 18 years of age or older found that only *69%* with could identify the current vice president.
statistic
Determine whether the underlined number describes a population parameter or a sample statistic. Explain your reasoning. *Sixty- five* of the 93 passengers aboard an airship survived an explosion.
the number is a population parameter because it is a numerical description of all of the passengers that survived
Determine whether the variable is qualitative or quantitative. Explain your reasoning. Distances between plants
the variable is quantitative because distances are numerical measurements
Determine whether the variable is qualitative or quantitative. Explain your reasoning. Heights of mountains in a region
the variable is quantitative because heights are numerical measurements
Determine whether the variable is qualitative or quantitative. Explain your reasoning. Wait times at hospital emergency departments
the variable is quantitative because wait times are numerical measurements
Determine whether the variable is qualitative or quantitative. Explain your reasoning. Wait times at banks
the variable is quantitative because waits times are numerical measurements
What is an inherent zero? Describe three examples of data sets that have inherent zeros and three that do not.
An inherent zero is a zero that implies none. HAVE 1.Average age of college students in years 2.Maximum wind speed during a hurricane 3.Average monthly precipitation in inches HAVE NOT 1.Temperature in degrees Fahrenheit 2.Average IQ score of a high school class 3.A student's level of happiness measured from 0 to 10
The graph to the right shows the average annual income in thousands for certain years. Identify the level of measurement of the data listed on the horizontal and vertical axes in the figure. Horizontal: Year Vertical: Annual income
Horizontal: interval Vertical: ratio
The graph to the right shows the average annual income in thousands for certain years. Identify the level of measurement of the data listed on the horizontal and vertical axes in the graph. Horizontal: Year Vertical: Annual income
Horizontal: interval Vertical: ratio
Determine if the survey question is biased. If the question is biased, suggest a better wording. How often do you eat carrots during an average month?
No, because it does not lead the respondent to any particular answer.
The ages of one person per row in a cinema
Sample, because the collection of ages of one person per row is a subset of all people in the cinema
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.
How is a sample related to a population?
a sample is a subset of a population
The number of children for each household in a town
Population, because it is a collection of the number of children for all households in the town.
The number of radios in each household in a country
Population, because it is a collection of the number of radios for all households in the country
In a poll, 1,004 adults 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, 46% said that they were in favor. Identify the population and the sample.
Population: all adults in the country Sample:1,004 adults selected
A survey of 12,081 women in a particular country found that 46.7% received an influenza vaccine for a recent flu season. Identify the population and the sample.
Population: the collection of immunization statuses of all women in the country Sample: the immunization status of the 12,081 women selected
A polling organization contacts 2636 undergraduates who attend a college and live outside the United States and asks whether or not they had taken a course in conversational English during their studies
Population: undergraduates who attend a college and live outside the US Sample:2636 undergraduates who attend a college and live outside the US
The region of a country with the highest level of food production for the past six years is shown below. Eastern Northeast Southern Eastern Eastern Eastern Determine whether the data are qualitative or quantitative and identify the data set's level of measurement.
Qualitative Nominal
The heights (in inches) of a sample of a species of tree two years after being planted are shown below. 21.5 19.1 23.2 20.4 20.1 21.3 21.7 18.5 22.2 Determine whether the data are qualitative or quantitative and identify the data set's level of measurement.
Quantitative Ratio
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
Venn Diagram: (1) population (2) sample
(1) the ages of home owners in the county (2) the ages of home owners in the county who work at home
Venn Diagram: (1) population (2) sample
(1) the income of home owners in the county (2) the income of home owners in the country who have a garage
Venn Diagram: (1) population (2) sample
(1) the incomes of home owners in the country (2) the income of home owners in the country who work at home
Identify the sampling techniques used, and discuss potential sources of bias (if any). Explain. After a wildfire, a disaster area is divided into 200 equal grids. Thirty of the grids are selected, and every occupied household in the grid is interviewed to help focus relief efforts on what residents require the most. (a)What type of sampling is used? (b) What potential sources of bias are present, if any? Select all that apply.
(a) Cluster sampling is used, since the disaster area is divided into grids, and some of those grids are selected and everyone in those grids is interviewed. (b) Certain grids may have been much more severely damaged than others. Severely damaged grids may have fewer occupied households.; Certain grids may have been much more severely damaged than others. The grids that are selected may not be representative in terms of damage
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 student union building, a researcher asks 372 students about their drinking habits. (a)What type of sampling is used? (b) What potential sources of bias are present, if any? Select all that apply.
(a) Convenience sampling is used, because students are chosen due to convenience of location. (b) Because of the personal nature of the question, students may not answer honestly.; The sample only consists of members of the population that are easy to get. These members may not be representative of the population.
Identify the sampling techniques used, and discuss potential sources of bias (if any). Explain. Chosen at random, 580 customers at a grocery store are contacted and asked their opinions of the service they received. (a)What type of sampling is used? (b) What potential sources of bias are present, if any? Select all that apply.
(a) Simple random sampling is used, since the business is selecting from its customers at random, and all samples of 580 customers have an equal chance of being selected. (b) The wording of the question asked to the customers may influence them towards a particular response. The results would not be usable in this case.
Identify the sampling techniques used, and discuss potential sources of bias (if any). Explain. In 1965, researchers used random digit dialing to call 1000 people and ask what obstacles kept them from eating healthier. (a) What type of sampling was used? (b) What potential sources of bias were present, if any? Select all that apply.
(a) Simple random sampling was used, since each number had an equal chance of being dialed, so all samples of 1000 phone numbers had an equal chance of being selected. (b) 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 51-acre field. The field is divided into one-acre subplots. A sample is taken from each subplot to estimate the harvest. (a)What type of sampling is used? (b) What potential sources of bias are present, if any? Select all that apply.
(a) Stratified sampling is used, since the field is divided into subplots and a random sample is taken from each subplot. (b) Certain subplots may have more or fewer lettuce plants than others. Samples from these subplots may bias the overall sample.
Identify the sampling techniques used, and discuss potential sources of bias (if any). Explain. Every fifteenth person entering a cafeteria is asked to choose his or her favorite meal from a list of five different meals that includes a description of each. (a)What type of sampling is used? (b) What potential sources of bias are present, if any? Select all that apply.
(a) Systematic sampling is used, because every fifteenth person is selected. (b) If there is a regular pattern to the people entering the cafeteria, the sample may not be representative.; The wording of the question may direct respondents towards a particular meal
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. Answer parts (a) through (c) below. (a)Identify the experimental units and treatments used in this experiment. Choose the correct answer below. (b) Identify a potential problem with the experiment design being used and suggest a way to improve it. Choose the correct answer below. (c) How could this experiment be designed to be a double-blind? Choose the correct answer below.
(a) The experimental units are the 30- to 35-year-old females being given the treatment. The treatment is the new allergy drug. (b)There may be a bias on the part of the researcher if the researcher knows which patients were given the real drug. (c) 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.
The following appear on a physician's intake form. Identify the level of measurement of the data. a)Change in health (scale of -5 to 5 (b)Marital status (c)Height (d)Year of birth
(a) ordinal (b) nominal (c) ratio (d) interval
In a recent study, volunteers who had 8 hours of sleep were three times more likely to answer questions correctly on a math test than were sleep-deprived participants. Complete parts a through d. (a) sample (b) sample's population (c) descriptive branch statement (d) inference based on results
(a) responses of the volunteers in the study (b)collection of the responses of all individuals who completed the math test (c)"three times more likely to answer the question correctly" (d) individuals who are not sleep deprived will be more likely to answer math questions correctly than individuals who are sleep deprived
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
Suppose a survey of 935 homeowners found that more than 25% bought flood insurance. Which part of the survey represents the descriptive branch of statistics? Make an inference based on the results of the survey.
Descriptive: 25% of homeowners in the sample bought flood insurance Inference: most homeowners do not buy flood insurance
A sample statistic will not change from sample to sample
FALSE-A sample statistic can change from sample to sample
A population is the collection of some outcomes, responses, measurements, or counts that are of interest
FALSE. A population is the collection of ALL outcomes, responses, measurements, or counts that are of interest
A statistic is a measure that describes a population characteristic
FALSE. A statistic is a measure that describes a sample characteristic
Data at the ordinal level are quantitative only.
FALSE. Data at the ordinal level can be qualitative or quantitative.
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.
Determine whether the statement is true or false. If it is false, rewrite it as a true statement. The method for selecting a stratified sample is to order a population in some way and then select members of the population at regular intervals.
False. The method for selecting a systematic sample is to order a population in some way and then select members of the population at regular intervals.
Determine whether the statement is true or false. If it is false, rewrite it as a true statement. Using a systematic sample guarantees that members of each group within a population will be sampled.
False. Using a stratified sample guarantees that members of each group within a population will be sampled.
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.
The years that your college football team won a championship. 1955 1965 1985 1986 1987 1993 2002 2007 2011 Determine the level of measurement of the data set. Explain your reasoning
Interval. The data can be ordered and differences between data entries are meaningful, but a zero entry is not an inherent zero.
The jersey numbers for players on a hockey team are listed below. Identify the level of measurement of the data set. Explain your reasoning.
Nominal. The data are categorized using numbers, but no mathematical computations can be made.
The top five bookstop five books on the best seller liston the best seller list last year arelast year are shown below. 1. The Forgotten 2. Gone Girl 3. Kiss The Dead 4. The Racketeer 5. Spring Fever Identify the level of measurement of the data set. Explain your reasoning.
Ordinal. The data can be arranged in order, but the differences between data entries are not meaningful.
Determine whether the underlined numerical value is a parameter or a statistic. Explain your reasoning. In a certain soccer league *43 %* of the 14 teams had won more games than they had lost.
Parameter, because the data set of all 14 teams is a population
Determine whether the underlined number is a statistic or a parameter. A sample of employees is selected and it is found that *35 %* own a computer.
Statistic because the value is a numerical measurement describing a characteristic of a sample
It is impossible for the Census Bureau to obtain all the census data about the population of the United States
TRUE
Determine if the survey question is biased. If the question is biased, suggest a better wording. Why is drinking soda bad for you?
The question is biased. The wording "How do you think drinking soda affects your health?" would be better.
Determine whether the following statement is true or false. If it is false, rewrite it as a true statement. A placebo is an actual treatment.
The statement is false. A placebo is a fake treatment.
Data at the ratio level cannot be put in order.
The statement is false. A true statement is "Data at the ratio level can be placed in a meaningful order."
For data at the interval level, you cannot calculate meaningful differences between data entries.
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 following statement is true or false. If it is false, rewrite it as a true statement. A double-blind experiment is used to increase the placebo effect.
The statement is false. Double blinding is used to decrease the placebo effect.
Determine whether the study is an observational study or an experiment. Explain. To study the effects of social media on teenagers' brains, researchers showed a few dozen teenagers photographs that had varying numbers of "likes" while scanning the reactions in their brains.
The study is an experiment, because it applies a treatment to the teenagers.
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 age of 75 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 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 most popular recording artist among 125,000 online movie rental subscribers.
The study would use a sampling. The study would use simple random sampling because it would be easy for the company to randomly select a portion of its subscribers
Determine whether the variable is qualitative or quantitative. Explain your reasoning. Time to finish a marathon
The variable is quantitative because time is found by measuring or counting.
Determine whether the variable is qualitative or quantitative. Explain your reasoning. Address
The variable is qualitative because an address describes an attribute or characteristic.
