MATH1040 Exam #1 Word Problems

Determine whether the statement is true or false. If it is false, rewrite it as a true statement. 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.

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.

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

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.

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

Determine whether the statement is true or false. If it is​ false, rewrite it as a true statement. In a frequency​ distribution, the class width is the distance between the lower and upper limits of a class.

False. In a frequency​ distribution, the class width is the distance between the lower or upper limits of consecutive classes.

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.

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 stratified sample guarantees that members of each group within a population will be sampled.

The following appears on a physician's intake form. Identify the level of measurement of the data. What is the level of measurement for "Year of birth"?

Interval

Why is a sample used more often than a population?

It is usually impossible to count the entire population.

After a flood, a disaster area is divided into 150 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. What type of sampling is used?

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.

Questioning students as they leave a university dorm, a researcher asks 353 students about their dating habits. What type of sampling is used?

Convenience sampling is​ used, because students are chosen due to convenience of location.

What are the two main branches of statistics?

Descriptive statistics and inferential statistics.

A graph shows the number of students in each sport at a high school. Horizontal Axes -- Sport Vertical Axes -- Number of Players Identify the level of measurement of the data listed on the horizontal axes in the figure.

Nominal

The following appears on a physician's intake form. Identify the level of measurement of the data. What is the level of measurement for "Marital status"?

Nominal

The region of a country with the highest level of food production for the past six years is shown below. Western, Northeast, Eastern, Southern, Northern, Southern What is the data set's level of measurement?

Nominal

Which levels of measurement for which data can be qualitative?

Nominal Ordinal

The list of books that your friends read for school for the past five months is shown below. Gone Girl, Private London, Spring Fever, Threat Vector, Kiss The Dead Identify the level of measurement of the data set. Explain your reasoning.

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 football 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 following appears on a physician's intake form. Identify the level of measurement of the data. What is the level of measurement for "Change in health (scale of -5 to 5)"?

Ordinal

Determine whether the underlined numerical value is a parameter of statistic. Explain your reasoning. A certain zoo found that __8%__ of its 843 animals were nocturnal.

Parameter, because the data set of all 843 animals were nocturnal.

Determine whether the data set is a population or a sample. Explain your reasoning. The age of each member of the Senate.

Population, because it is a collection of ages for all members of the Senate.

Determine whether the data set is a population or a sample. Explain your reasoning. The salary of each baseball player in a league.

Population, because it is a collection of salaries for all baseball players in the league.

The region of a country with the highest level of food production for the past six years is shown below. Western, Northeast, Eastern, Southern, Northern, Southern Are the data qualitative or quantitative?

Qualitative

Determine whether the variable is qualitative or quantitative. Explain your reasoning. Places of birth The variable is ______________ because places are _________________.

Qualitative, attributes or labels

Determine whether the variable is qualitative or quantitative. Explain your reasoning. Responses on an opinion poll The variable is ______________ because responses are _______________.

Qualitative, attributes or labels

The lengths (in inches) of a sample of a species of fish caught in the waters of a region are shown below. 20.8, 18.2, 20.3, 22.9, 21.9, 22.5, 20.1, 19.1, 20.9 Are the data qualitative or quantitative?

Quantitative

Describe the relationship between quartiles and percentiles. ____________ are special cases of ____________. ______ is the 25th percentile, ______ is the 50th percentile, and ______ is the 75th percentile.

Quartiles, Percentiles, Q1, Q2, Q3

A graph shows the number of students in each sport at a high school. Horizontal Axes -- Sport Vertical Axes -- Number of Players Identify the level of measurement of the data listed on the vertical axes in the figure.

Ratio

The following appears on a physician's intake form. Identify the level of measurement of the data. What is the level of measurement for "Time since the last visit"?

Ratio

The lengths (in inches) of a sample of a species of fish caught in the waters of a region are shown below. 20.8, 18.2, 20.3, 22.9, 21.9, 22.5, 20.1, 19.1, 20.9 What is the data set's level of measurement?

Ratio

What is the difference between relative frequency and cumulative frequency?

Relative frequency of a class is the percentage of the data that falls in that​ class, while cumulative frequency of a class is the sum of the frequencies of that class and all previous classes.

Determine whether the data set is a population or a sample. Explain your reasoning. The ages of three families of people in an apartment building housing ten families.

Sample, because the collection of ages for three families of people is a subset of all people living in the building.

Chosen at random, 680 customers at a department store are contacted and asked their opinions of the service they received. What type of sampling is used?

Simple random sampling is​ used, since the business is selecting from its customers at​ random, and all samples of 680 customers have an equal chance of being selected.

In 1965, researchers used random digit dialing to call 1000 people and ask what obstacles kept them from eating healthier. 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 1000 phone numbers had an equal chance of being selected.

Determine whether the underlined numerical value is a parameter of statistic. A sample of seniors is selected and it is found that ___25%___ own a television.

Statistic because the value is a numerical measurement describing a characteristic of a sample.

What is an advantage of using a​ stem-and-leaf plot instead of a​ histogram?

Stem-and-leaf plots contain original data values where histograms do not.

Corn is planted on a 52-acre field. The field is divided into one-acre subplots. A sample is taken from each subplot to estimate the harvest. What type of sampling is used?

Stratified sampling is​ used, since the field is divided into subplots and a random sample is taken from each subplot.

Every eighth person entering a library is asked to choose his or her favorite author from a list of five different authors that includes a description of each. What type of sampling is used?

Systematic sampling is​ used, because every eighth person is selected.

A quality-control manager randomly selects 70 bottles of orange juice that were filled on July 5 to assess the calibration of the filling machine. What is the sample is the study?

The 70 bottles of orange juice selected in the plant on July 5.

What is a difference between the Empirical Rule and​ Chebychev's Theorem?

The Empirical Rule assumes the distribution is aproximately symmetric and​ bell-shaped and​ Chebychev's Theorem makes no assumptions.

How is a Pareto chart different from a standard vertical bar​ graph?

The bars are positioned in order of decreasing height with the tallest bar on the left.`

A survey of 12,084 women in a particular country found that 47.8% received an influenza vaccine for a recent flu season. Identify the population and the sample. Identify the population for the given problem.

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

A survey of 12,084 women in a particular country found that 47.8% received an influenza vaccine for a recent flu season. Identify the population and the sample. Identify the sample for the given problem.

The immunization status of the 12,084 women selected.

Use the Venn diagram to identify the population and the sample. The smaller blue box inside of the big grey box -- The income of homeowners in the county who work at home. The large grey box encompassing the blue box -- The income of homeowners in a certain county Choose the correct description of the sample.

The income of homeowners in the county who work at home.

Use the Venn diagram to identify the population and the sample. The smaller blue box inside of the big grey box -- The income of homeowners in the county who work at home. The large grey box encompassing the blue box -- The income of homeowners in a certain county. Choose the correct description of the population.

The income of homeowners in the county.

Determine if the survey question is biased. If the question is biased, suggest a better wording. Why is drinking fruit juice good for you?

The question is biased. The wording​ "How do you think drinking fruit juice affects your​ health?" would be better.

Determine whether the approximate shape of the distribution in the histogram shown is​ symmetric, uniform, skewed​ left, skewed​ right, or none of these. Justify your answer. The tops of all of the bars are almost equal with slight alterations between each.

The shape of the distribution is approximately uniform because the bars are approximately the same height.

Determine whether the approximate shape of the distribution in the histogram shown is​ symmetric, uniform, skewed​ left, skewed​ right, or none of these. Justify your answer. A graph that has an L-shape.

The shape of the distribution is skewed right because the bars have a tail to the right.

Explain the relationship between variance and standard deviation. Can either of these measures be​ negative? Explain.

The standard deviation is the positive square root of the variance. The standard deviation and variance can never be negative. Squared deviations can never be negative.

Determine whether the 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.

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

Determine whether the 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.

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

Determine whether the 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.

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 statement is true or false. If it is​ false, rewrite it as a true statement. Some quantitative data sets do not have medians.

The statement is false. All quantitative data set have medians.

Determine whether the statement is true or false. If it is​ false, rewrite it as a true statement. An ogive is a graph that displays relative frequencies.

The statement is false. An ogive is a graph that displays cumulative frequencies.

Determine whether the statement is true or false. If it is​ false, rewrite it as a true statement. It is impossible to have a​ z-score of 0.

The statement is false. A​ z-score of 0 is a standardized value that is equal to the mean.

Determine whether the statement is true or false. If it is​ false, rewrite it as a true statement. The 50th percentile is equivalent to Q1.

The statement is false. The 50th percentile is equivalent to Q2.

Determine whether the following statement is true or false. If it is​ false, rewrite it as a true statement. The mean is the measure of central tendency most likely to be affected by an outlier.

The statement is true.

Determine whether the statement is true or false. If it is​ false, rewrite it as a true statement. A data set can have the same​ mean, median, and mode.

The statement is true.

Determine whether the statement is true or false. If it is​ false, rewrite it as a true statement. The midpoint of a class is the sum of its lower and upper limits divided by two.

The statement is true.

Determine whether the statement is true or false. If it is​ false, rewrite it as a true statement. When each data class has the same​ frequency, the distribution is symmetric.

The statement is true.

A​ student's score on an actuarial exam is in the 78th percentile. What can you conclude about the​ student's exam​ score?

The student scored higher than​ 78% of the students who took the actuarial exam.

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 car color among the 65 residents of a retirement community.

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

The goals scored per game by a soccer team represent the first quartile for all teams in a league. What can you conclude about the​ team's goals scored per​ game?

The team scored fewer goals per game than​ 75% of the teams in the league.

Determine whether the variable is qualitative or quantitative. Explain your reasoning. Favorite song

The variable is qualitative because a favorite song describes an attribute or characteristic.

Determine whether the variable is qualitative or quantitative. Explain your reasoning. Breed of dog

The variable is qualitative because breed describes an attribute or characteristic.

Determine whether the variable is qualitative or quantitative. Explain your reasoning. Favorite color

The variable is qualitative because color describes an attribute or characteristic.

Suppose a survey of 521 women in the US found that more than 56% 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 inference from the given information.

There is an association between US women and being the primary investor in their household.

For the month of​ April, a checking account has a balance of $586 for 23 days, $2,463 for 2 days​, and $271 for 5 days. What is the​ account's mean daily balance for​ April?

The​ account's mean daily balance for April is approximately $658.63.

Determine whether the statement is true or false. If it is false rewrite it as a true statement An outlier is any number above Q3 or below Q1.

This statement is false. A true statement is​ "An outlier is any number above Q3+​1.5(IQR) or below Q1−​1.5(IQR) are considered​ outliers."

Determine whether the statement is true or false. If it is​ false, rewrite it as a true statement. The second quartile is the median of an ordered data set.

True

Determine if the survey question is biased. If the question is biased, suggest a better wording. How often do you go out walking during an average week?

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

Questioning students as they leave a university dorm, a researcher asks 353 students about their dating habits. What potential sources of bias are present, if any?

- 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.

In terms of displaying​ data, how is a​ stem-and-leaf plot similar to a dot​ plot?

- Both plots show how data are distributed. - Both plots can be used to identify unusual data values. - Both plots can be used to determine specific data entries.

After a flood, a disaster area is divided into 150 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. What potential sources of bias are present, if any?

- 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.

Corn is planted on a 52-acre field. The field is divided into one-acre subplots. A sample is taken from each subplot to estimate the harvest. What potential sources of bias are present, if any?

- Certain subplots may have more or fewer corn plants than others. Samples from these subplots may bias the overall sample.

Every eighth person entering a library is asked to choose his or her favorite author from a list of five different authors that includes a description of each. What potential sources of bias are present, if any?

- If there is a regular pattern to the people entering the library​, the sample may not be representative. - The wording of the question may direct respondents towards a particular author.

In 1965, researchers used random digit dialing to call 1000 people and ask what obstacles kept them from eating healthier. What potential sources of bias were present, if any?

- Individuals may have not been available when the researchers were calling. Those individuals that were available may have not been representative of the population. - 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.

Chosen at random, 680 customers at a department store are contacted and asked their opinions of the service they received. What potential sources of bias are present, if any?

- 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.

Suppose a survey of 521 women in the US found that more than 56% 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.

56% of women in the sample are the primary investor in their household.

Explain how the interquartile range of a data set can be used to identify outliers The interquartile range​ (IQR) of a data set can be used to identify outliers because data values that are ____________ , ____________, or ____________, ____________ are considered outliers.

greater than, Q3 + 1.5(IQR), less than, Q1 - 1.5(IQR)

What is the difference between a parameter and a statistic? A parameter is a numerical description of a __________ characteristic. A statistic is a numerical description of a ___________ characteristic.

population, sample

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 frequency polygon and an ogive?

A frequency polygon displays class frequencies while an ogive displays cumulative frequencies.

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 orange juice that were filled on July 5 to assess the calibration of the filling machine. What is the population in the study?

All bottles of orange juice produced in the plant on July 5.

Discuss the similarities and the differences between the Empirical Rule and​ Chebychev's Theorem.

Both estimate proportions of the data contained within k standard deviations of the mean.

What is a disadvantage of using a​ stem-and-leaf plot instead of a​ histogram?

Histograms easily organize data of all sizes where​ stem-and-leaf plots do not.

Why should the number of classes in a frequency distribution be between 5 and 20?

If the number of classes in a frequency distribution is not between 5 and​ 20, it may be difficult to detect any patterns.

Describe the difference between the calculation of population standard deviation and that of sample standard deviation. Let N be the number of data entries in a population and n be the number of data entries in a sample data set. Choose the correct answer below.

When calculating the population standard​ deviation, the sum of the squared deviation is divided by​ N, then the square root of the result is taken. When calculating the sample standard​ deviation, the sum of the squared deviations is divided by n−​1, then the square root of the result is taken.

Given a data​ set, how do you know whether to calculate σ or​ s?

When given a data​ set, one would have to determine if it represented the population or if it was a sample taken from the population. If the data are a​ population, then σ is calculated. If the data are a​ sample, then s is calculated.