E370 Exam 1

primary data

data that you have collected for your own use

correlation coefficient numbers

- 1:1

mean > median

right skewed

Suppose the dealer incentive per vehicle for Honda's Acura brand is thought to be bell-shaped and symmetrical with a mean of $2,500 and a standard deviation of $300. Based on this information, what interval of dealer incentives would we expect approximately 99.7% of vehicles to fall within? $1,600 to $3,400 $1,900 to $3,100 $2,200 to $2,800 $1,300 to $3,700

$1,600 to $3,400

bar charts

- can be arranged in a vertical or horizontal orientation - on one axis (usually horizontal), we specify the labels that are used for each of the classes -A frequency or relative frequency scale can be used for the other axis (usually, vertical) - Using a bar of fixed width drawn above each class label, we extend the height appropriately

disadvantages of primary data

- can be expensive and time consuming to gather

advantages of primary data

- collected by the person or organization who uses the data

What type of relationship is indicated in the scatterplot? It is hard to tell because the variables are not identified A negative relationship No relationship A positive relationship

A negative relationship

Which of the following is a quantitative variable? House age All of the suggested choices House price House size

All of the suggested choices

descriptive statistics

Collecting, summarizing, and displaying data (reported based on observations)

Advantages of range

Easy to calculate

Conditional Probability Formula

P(A | B) = P(A and B) / P(B) or P (A | B) = P( A ∩ B) / P(B)

correlation coefficient

The sample correlation coefficient, rxy , indicates both the strength is and direction of the linear relationship between the independent and dependent variables:

positive z score

above the mean

estimated class width formula

max data value - min data value / k

z scores from -3 to 3

outliars

wide classes result in few class intervals

- can obscure important patterns - gives a blocky distribution graph - tells little about the distribution shape

primary data collection methods

- direct observations - experiments - survey's

disadvantages of secondary data

- no control over how the data was collected - less reliable unless collected and recorded accurately

advantages of secondary data

- readily available - less expensive to collect

too many narrow classes in a histogram also have consequences

- results in a jagged histogram - some classes may be empty

the need for sampling

- too expensive to gather info on the entire pop - too time consuming to gather info on the entire pop - often impossible to gather info on the entire pop

Cross-section data

- values collected from a number of subjects during a single time period - subjects might include individuals, households, firms, industries, regions, countries

time series data

- values that correspond to specific measurements taken over a range of time periods - data can include hourly, weekly, monthly, quarterly, or annual observations

class width

-The width is the range of numbers to put into each class - Round this estimate to a useful whole number that makes the frequency distribution more readable -There is no one correct answer for the class width - The goal is to create a histogram to clearly and usefully show the pattern in the data - Often there is more than one acceptable way to accomplish this

In a standard normal distribution, the probability that z is greater than zero is 1 1.96 0.5 at least 0.5

.5

probability of discrete probability distributions must be between

0 and 1

ideal number of classes in a frequency distribution

4-20 - Some data sets, particularly those with continuous data, require several values to be grouped together in a single class - This grouping prevents having too many classes in the frequency distribution, which can make it difficult to detect patterns

a binomial random variable

A binomial random variable is defined as the number of successes denoted by x achieved in the n trials and is a result of a Binomial Experiment Characteristics of a Binomial Experiment: 1. The experiment consists of a fixed number of (Bernoulli) trials, denoted by n 2. Each trial has only two possible outcomes, a success and a failure 3. The probability of a success p and the probability of a failure q are constant throughout the experiment 4. Each trial is independent of the other trials in the experiment

Scatterplot

A scatter plot is a graphical tool used to determine if two variables are related. Each point represents a pair of known values of the two variables for one observation In the relationship, we usually distinguish between dependent and independent variables

complement of an event

All possible outcomes that are not in the event P(A) + P(A' ) = 1 or P(A) = 1 - P(A' )

empirical method of probability

Assigning probabilities based on experimentation or historical data 𝑃 𝐴 = Frequency in which Event A occurs / Total number of observations

subjective method of probability

Assigning probabilities based on judgment or experience

classical method of probability

Assigning probabilities based on the assumption of equally likely outcomes 𝑃 𝐴 = Number of possible outcomes that constitute Event A / Total number of possible outcomes in the sample space

addition rule for mutually exclusive events formula

If A and B are mutually exclusive, P(A or B) = P(A) + P(B) or P (A∩B) = P(A)+P(B)

multiplication rule for dependent events

P(A I B) = P(A∩B)/P(B) or 𝑃 𝐴∩𝐵 =𝑃 𝐵 𝑃(𝐴|𝐵)

Addition Rule for Probability formula

P(A or B) = P(A) + P(B) -P(A and B) or P(A ∩ B) = P(A) + P(B) -P(A ∩B)

pie charts

Pie charts are a tool for comparing proportions for qualitative data Each segment of the pie represents the relative frequency of one category - All categories in the data set must be included in the pie - Use a pie chart to compare the relative sizes of all possible categories - Bar charts are more useful when you want to highlight the actual data values

the intersection of events

The intersection of events A and B is the set of all outcomes that are in both A and B The intersection of events A and B is denoted by A ∩ B

Mean of a discrete probability distribution

The mean, 𝝁, of a discrete probability distribution is the weighted average of ALL values of the random variable • The weights are the probabilitie s• The mean does not have to be a value the random variable can assume Mean is also known as the expected value E(x)

the multiplication rule

The multiplication rule is used to determine the probability of the intersection (joint probability) of two events occurring, or P(A and B)

independent events

The outcome of one event does not affect the outcome of the second event P (A | B) = P(A)

Conditional Probability

The probability of an event given or knowing that another event has occurred is called a conditional probability The conditional probability of A given B is denoted by P(A|B) and computed as:

Percentile

The pth percentile divides a data set into two parts: • Approximately p percent of the observations have values less than the pth percentile • Approximately (100 − p) percent of the observations have values greater than the pth percentile

Sample Mean Formula

The sample mean formula is: x̄ = ( Σ xi ) / n x̄ just stands for the "sample mean" Σ means "add up" xi "all of the x-values" n means "the number of items in the sample" Finding the mean To find the mean, sum all the numbers and then divide by the number of items in the set. For example, to find the mean of the following set of numbers: 21, 23, 24, 26, 28, 29, 30, 31, 33 First add them all together: 21 + 23 + 24 + 26 + 28 + 29 + 30 + 31 + 33 = 245 Then divide your answer by the number of items in your set. There are 9 numbers, so: 245 / 9 = 27.222

the union of events

The union of events A and B is the event containing all outcomes that are in A or B or both The union of events A and B is denoted by A U B

mutually exclusive events

Two events are said to be mutually exclusive if the events have no outcomes in common Two events are mutually exclusive if, when one event occurs, the other cannot occur

Parameter

a described characteristic about a population

Statistic

a described characteristic about a sample

random variable

a numerical description of the outcome of an experiment

data set

all the data collected in a particular study

Elements

are the entities on which data are collected

negative z-score

below the mean

if data has exactly 2 modes

bimodal

The standard deviation of a sample of 100 elements taken from a very large population is determined to be 60. The variance of the population must be at least 100 can be any value greater than zero cannot be larger than 3600 cannot be larger than 60

can be any value greater than zero

qualitative data

classified by descriptive terms (labels or names used to identify an attribute of elements) examples: - hair color - eye color - political party - marital status

Measures of Relative Position

compare the position of one value in relation to other values in the data set

secondary data

data collected by someone else

information

data that are transformed into useful facts that can be used for a specific purpose, such as making a decision it is more than just data

quantitative data

described by numerical values (how many or how much) 1. counted: - number of children - defects per hour 2. measured: - weight - voltage

The Department of Transportation of a city has noted that on the average there are 17 accidents per day. The average number of accidents is an example of descriptive or inferential statistic?

descriptive

probability distributions can be

discrete or continous

relative frequency distribution

displays the proportion of observations of each class relative to the total number of observations - shows the fraction of observations in each class - found by dividing each frequency by the total number of observations - fractions in a relative frequency distribution add up to 1

tabular data

frequency distribution, relative frequency distribution, and cumulative relative frequency distribution

graph data

histogram

mutually exclusive events does not equal

independent events • If one mutually exclusive event is known to occur, the other cannot occur. thus, the probability of the other event occurring is reduced to zero (and they are therefore dependent)

Based on a survey, it was concluded that households with children under the age of 18 are more likely to have access to the Internet than family households with no children. Is it an example of descriptive or inferential statistic?

inferential

2 types of quantitative data

interval and ratio

a variable

is a characteristic of interest for the elements

Histogram

is a graph showing the number or % of observations in each class - it is a graphical representation of a frequency distribution or the relative frequency distribution - classes of a variable of interest are placed on the horizontal axis - a rectangle is drawn above each class interval with its height corresponding to the frequency or relative frequency

classes letter

k

mean < median

left skewed

inferential statistics

making claims or conclusions about the population based on a sample of data sample statistic is calculated form the sample data and is used to make inferences about the unknown pop parameter

a continuous random variable

may assume any numerical value in an interval or collection of intervals • Often measured, fractional values are possible • time required to complete a task; height; distance

a discrete random variable

may assume either a finite number of values or an infinite sequence of values • Values are whole numbers (integers), usually counted • number of complaints per day; number of TVs in a household

Which of the following is the most influenced by outliers? Median 75th percentile 1st quartile Mean

mean

central tendency

mean, median, mode

coefficient of variance

measures the SD in terms of its percentage of the mean and indicates how large the SD is in relation to the mean • A high CV indicates high variability relative to the mean • A low CV indicates low variability relative to the mean

When outliers are present in the data set, which measure is the best to describe central tendency in the data? weighted mean median mean standard deviation

median

The median is defined as the most frequent value of a data set middle point in a data set average of a data set closest value to the mean

middle point in a data set

if the data has more than 2 modes

multimodal

The normal distribution can well approximate the binomial distribution as long as n q ≥ 5 n p ≥ 5 , n q ≥ 5 n p ≥ 5 We do not need any additional requirements because it is always the case

n p ≥ 5 , n q ≥ 5

negative sample covariance

negative linear relationship

2 types of qualitative data

nominal and ordinal

2 measures of relative position

percentiles and quartiles

positive sample covariance

positive linear relationship

Addition Rule of Probability

provides a way to compute the probability of event A, or B, or both A and B occurring

nominal data

qualitative arbitrary labels for data. no ranking allowed examples: - eye color - zip code

ordinal data

qualitative ranking allowed. no measurable meaning to the number of differences example: - education level

interval data

quantitative meaningful differences. no true point zero (zero does not mean absence) example: - calendar year

ratio data

quantitative meaningful differences. true zero point (zero means absence) example: - income (48,000 or 0)

measures of variability

range, variance, standard deviation

sample

refers to a portion of the population that is representative of the population form which it was selected

class boundaries

represent min and max values for each class

Population

represents all possible subjects that are of interest in a particular study

Sample Variance Formula

s^2 = ∑(x- x̄)^2 / n-1 s^2 is the sample variance x is the value of each observation in the sample x̄ is the mean of the sample n is the number of observations in the sample

zero z score

same as mean

measures of association between 2 variables

sample covariance and sample correlation coefficient

frequency distribution

shows the number of data observations that fall into specific intervals

Quartiles

split the ranked data into 4 equal groups:• The first quartile (Q1) is the value that constitutes the 25th percentile • The second quartile (Q2) is the value that constitutes the 50th percentile • Second quartile (the 50th percentile) = Median • The third quartile (Q3) is the value that constitutes the 75th percentile

Sample Covariance

sxy , measures the direction of the linear relationship between two variables

mean = median

symmetrical distribution

sample variance

s²

Z Scores are ...

the # of standard deviations above or below the mean

the sample variance is

the average of the squared differences between each data value and the mean

Statistics

the mathematical science that deals with the collection, analysis, and presentation of data, which can then be used as a basis for inference and induction

If no data value or category repeats more than once, then we say that

the mode does not exist

observation

the set of measurements obtained for a particular element "a data set with n elements contains n observations"

if the sample covariance is 0

there is no linear relationship

cumulative relative frequency distribution

totals the proportion of observations that fall below the upper limit of each class - shows the accumulated proportion as a class values vary from low to high - cumulative relative frequency for the highest class is equal to 1

Data

values assigned to observations or measurements

Weighted Mean Formula

x bar = ∑ (w • x) / ∑w

Population Mean Formula

μ = ( Σ X ) / N

Which of the following symbols represents the standard deviation of the population? μ σ σ 2 x ¯

σ

disadvantages of range

• Based on two numbers in the data set and ignores the way in which the data are distributed • Sensitive to outliers Change in one value causes a dramatic change in the range The range does not accurately reflect the overall variability of the data

advantages of weighted mean

• Simple to calculate • Summarizes the data with a single value

disadvantages of weighted mean

• With only a summary value we lose information about the original data • The value of the mean is sensitive to outliers (values that are much higher or lower than most of the data)

a discrete probability distribution is

• a listing of all the possible outcomes of an experiment for a discrete random variable • along with the relative frequency of each outcome

discrete probability distribution

• describes how probabilities are distributed over the values of the random variable • can be represented by a table, a graph, or a formula • a formula used to describe discrete probability distribution is called a probability function, denoted by P(x) (sometimes f(x)), which provides the probability for each value of the random variable x

multiplication rule for independent events

𝑃 𝐴∩𝐵 =𝑃 𝐵 𝑃(𝐴)

Which one of the following is NOT a valid number for a probability? 0 1.5 0.63 17%

1.5

x is a random variable with the probability function P(x) = x/6 for x = 1, 2 or 3. The expected value of x is 0.5 2 2.333 0.333

2.333

Consider the following frequency distribution: Class Frequency 12 up to 15 3 15 up to 18 6 18 up to 21 3 21 up to 24 4 24 up to 27 4 The total number of observations to construct this frequency distribution is 20 24 6 4

20

Twenty percent of the students in a class of 100 are planning to go to graduate school. The standard deviation of this binomial distribution is 20 4 2 16

4

The statistics professor has kept attendance records and recorded the number of absent students per class. The recorded data is displayed in the following bar chart with the frequency of each number of absent students shown above the bars. How many statistics classes had three or more students absent? 43 22 8 13

43

Assume that you have a binomial experiment with p = 0.5 and a sample size of 100. The expected value for this distribution is 50 100 5 0.5

50

Suppose the wait through immigration at JFK Airport in New York is thought to be bell-shaped and symmetrical distributed with a mean of 22 minutes. It is known that 68 percent of travelers will spend between 16 and 28 minutes waiting to pass through immigration. The standard deviation for the wait time through immigration is 10 minutes 12 minutes 8 minutes 6 minutes

6 minutes

An analyst constructed the following frequency distribution on the monthly returns for 50 selected stocks: Class (in percent) Frequency -10 up to 0 8 0 up to 10 25 10 up to 20 15 20 up to 30 2 The cumulative relative frequency for the class "0 up to 10" is 0.66. This means that 66% of stocks have returns above 10% 66% of stocks have returns below 10% 66% of stocks have returns below 0% 66% of stocks have returns between 0% and 10%

66% of stocks have returns below 10%

The following data represent the recent sales price (in $1,000s) of 24 homes in a Midwestern city:187 125 165 170 230 139 195 229239 135 188 210 228 172 127 139122 181 196 237 115 199 170 239Suppose the data are grouped into five classes, and one of them will be "165 up to 190." The frequency of this class is 7 6 6/24 7/24

7

The following data represent the recent sales price (in $1,000s) of 24 homes in a Midwestern city:187 125 165 170 230 139 195 229239 135 188 210 228 172 127 139122 181 196 237 115 199 170 239Suppose the data are grouped into five classes, and one of them will be "115 up to 140." The relative frequency of this class is 6/24 7/24 6 7

7/24

What is probability? A numerical value assigned to an event that measures the number of its occurrences A value between 0 and 1 assigned to an event that measures the likelihood of its occurrence A value between 0 and 1 assigned to an event that measures the unlikelihood of its occurrence Any value between 0 and 1 randomly assigned to an event

A value between 0 and 1 assigned to an event that measures the likelihood of its occurrence

The accompanying chart shows the numbers of books written by each author in a collection of cookbooks. What type of chart is this? Histogram for qualitative data Bar chart for quantitative data Bar chart for qualitative data Histogram for quantitative data

Bar chart for qualitative data

How do we find the median if the number of observations in a data set is odd? By taking the middle value in the sorted data set after eliminating outliers By averaging the first and the third quartiles By taking the middle value in the sorted data set By averaging the minimum and maximum values

By taking the middle value in the sorted data set

Which of the following variables is qualitative? Weight Gender Temperature Height

Gender

Which one of the following statements about probability in NOT true? If Events A and B are mutually exclusive, then Event A and Event B must occur at the same time during the experiment If P(A) = 1, then with certainty, Event A must occur The probabiity of any event must range between 0 and 1 If P(A) = 0, then with certainty, Event A will not occur

If Events A and B are mutually exclusive, then Event A and Event B must occur at the same time during the experiment

Suppose that you conduct a study in which you observe parents and their children interacting at home. You find that the more supportive parents are, the less aggressive their children are. What conclusion can you make? Level of support and aggression are negatively correlated. Children being aggressive causes parents to be less supportive. Parents being more supportive causes children to be less aggressive. Level of support and aggression are positively correlated.

Level of support and aggression are negatively correlated.

The Boom company has recently decided to raise the salaries of all employees by 10%. Which of the following is(are) expected to be affected by this raise? Mode and median only Mean, median, and mode Mean and mode only Mean and median only

Mean, median, and mode

Frequency distributions may be used to describe which of the following types of data? Nominal, ordinal, interval, and ratio data Nominal, ordinal, and interval data only Nominal and ordinal data only Nominal and interval data only

Nominal, ordinal, interval, and ratio data

If two groups of numbers have the same mean, then their standard deviations must also be equal None of the suggested alternatives is correct their modes must also be equal their medians must also be equal

None of the suggested alternatives is correct

The mean of the sample can never be negative is always smaller than the mean of the population from which the sample was taken can never be zero None of the suggested alternatives is correct

None of the suggested alternatives is correct

It is known that the length of a certain product x is normally distributed with µ = 20 inches. How is the probability P ( x > 16 ) related to P ( x < 16 )? P ( x > 16 )is smaller than P ( x < 16 ) No comparison can be made with the given information P ( x > 16 )is greater than P ( x < 16 ) P ( x > 16 )is the same as P ( x < 16 )

P ( x > 16 )is greater than P ( x < 16 )

If x has a normal distribution with µ = 100 and σ = 5, then the probability P ( 90 ≤ x ≤ 95 ) can be expressed in terms of a standard normal variable z as P ( − 2 ≤ z ≤ − 1 ) P ( − 2 ≤ z ≤ − 2 ) P ( − 2 ≤ z ≤ 1 ) P ( 2 ≤ z ≤ 1 )

P ( − 2 ≤ z ≤ − 1 )

The accompanying chart shows the numbers of books written by each author in a collection of cookbooks. What type of data is being represented? Qualitative, ordinal Qualitative, nominal Quantitative, interval Quantitative, ratio

Qualitative, nominal

Which of the following is an example of time series data? Quarterly housing starts collected over the last 60 years Starting salaries of recent business graduates at IU Results of market research conducted in 2012 testing consumer preferences for soda The sale prices of townhouses sold last year

Quarterly housing starts collected over the last 60 years

Which of the following represents a population and a sample from that population? Freshmen at IU and basketball players at IU Teachers of a high school and members of the parent-teacher group Fans at a concert who purchase T-shirts, and fans at a concert who purchase soda Residents of Albany, New York, and registered voters in Albany, New York

Residents of Albany, New York, and registered voters in Albany, New York

Which of the following is an example of cross-sectional data? Quarterly housing starts collected over the last 60 years Daily price of DuPont stock during the first quarter Results of market research conducted in 2012 testing consumer preferences for soda GDP of the United States from 1990-2010

Results of market research conducted in 2012 testing consumer preferences for soda

Which of the following can be represented by a discrete random variable? The average outside temperature taken every day for two weeks The height of college students The number of obtained spots when rolling a six-sided die The finishing time of participants in a cross-country meet

The number of obtained spots when rolling a six-sided die

Which of the following is NOT a characteristic of a binomial experiment? The probability of a success must exceed the probability of a failure. Each trial is independent of the other trials in the experiment. Each trial has only two possible outcomes—a success or a failure. The experiment consists of a fixed number of trials.

The probability of a success must exceed the probability of a failure.

Which of the following is NOT a characteristic of the normal probability distribution? The mean of the distribution can be negative, zero, or positive The distribution is symmetrical The standard deviation must be 1 The mean, median, and the mode are equal

The standard deviation must be 1

Which of the following can be represented by a continuous random variable? The score of a randomly selected student on a five-question multiple-choice quiz The number of defective light bulbs in a sample of five The number of arrivals to a drive-through bank window in a four-hour period The time of a flight between Chicago and New York

The time of a flight between Chicago and New York

Is it possible for a data set to have more than one mode? No, there must always be a single mode, or else there is no mode. Yes, if there are at least two different values in a data set, there is always more than one mode. Yes, if two or more values in a data set occur the same number of times. Yes, if two or more values in a data set occur with the most frequency.

Yes, if two or more values in a data set occur with the most frequency.

Positive values of the correlation coefficient indicate a positive variance of the x values a positive relation between the independent and the dependent variables a positive variance of the y values that the standard deviations of both x and y are positive

a positive relation between the independent and the dependent variables

A population consists of a subject of interest in a sample all items of interest in a sample a subject of interest in a study all items of interest in a study

all items of interest in a study

A survey asked randomly selected adults 18-29 years old to indicate their working status. The results are shown in the following table: Working Status Frequency Working full-time 103 Working part-time 60 Student, not working 31 Unemployed 56 The probability that a randomly selected adult 18-29 years old is unemployed calculated using this data would be an empirical probability a classical probability a subjective probability a simple probability

an empirical probability

A continuous random variable may assume only the positive integer values in an interval only integer values in an interval or collection of intervals any value in an interval or collection of intervals only fractional values in an interval or collection of intervals

any value in an interval or collection of intervals

Population parameters are difficult to calculate due to the infeasibility of collecting data on the entire population the fact that samples are difficult to draw due to the nature of the data cost prohibitions on data collection both cost prohibitions on data collection and the infeasibility of collecting data on the entire population

both cost prohibitions on data collection and the infeasibility of collecting data on the entire population

Comparing the consistency (variability) between two data sets when their means are very different is best done with the coefficient of variation z-score standard deviation median

coefficient of variation

Since the population is always larger than the sample, the value of the sample mean is always larger than the true value of the population mean could be larger, equal to, or smaller than the true value of the population mean is always smaller than the true value of the population mean is always equal to the true value of the population mean

could be larger, equal to, or smaller than the true value of the population mean

Which of the following measures the direction of the linear relationship between two variables but does not measure the strength of the relationship? variance coefficient of variation covariance correlation coefficient

covariance

Suppose that you obtained the following scatter plot for the relationship between variables x and y. What would you conclude about sample covariance for this data? covariance is negative covariance is negative and close to -1 covariance can take any value covariance is negative and close to 0

covariance is negative

Your business statistics class had a test last week. The average score for the class is an example of secondary data descriptive statistics qualitative data inferential statistics

descriptive statistics

The Law of Large Numbers states that when an experiment is conducted a large number of times, the [ Select ] ["empirical", "subjective", "classical"] probabilities of the process will converge to the [ Select ] ["subjective", "empirical", "classical"] probabilities.

empirical classical

In inferential statistics, we calculate sample statistics to Neither of suggested choices is correct summarize the information about the sample make conclusions about the sample estimate unknown population parameters

estimate unknown population parameters

A qualitative variable assumes meaningful numerical values.

false

Cross-sectional data contain values of a characteristic of one subject collected over time.

false

Nominal data has all the features of interval data with the added benefit of having a true zero point.

false

Population parameters are used to estimate corresponding sample statistics.

false

The branch of statistical studies called inferential statistics refers to drawing conclusions about sample data by analyzing the corresponding population.

false

The mathematical operation of addition can be performed on nominal data.

false

Typically, it is possible to examine every member of the population.

false

Which scales of data measurement are associated with quantitative data? Interval and ratio Ratio and nominal Nominal and ordinal Ordinal and interval

interval and ratio

The Fahrenheit scale for measuring temperature would be classified as a(n) nominal scale ratio scale ordinal scale interval scale

interval scale

If a data set has an even number of observations, the median is the average value of the two middle items is the average value of the two middle items when all items are arranged in ascending order cannot be determined must be equal to the mean

is the average value of the two middle items when all items are arranged in ascending order

The center of a normal curve is always equal to zero cannot be negative is the mean of the distribution is the standard deviation

is the mean of the distribution

The covariance ranges between minus infinity and plus infinity 0 and 1 0 and 100 -1 and +1

minus infinity and plus infinity

Which measure would you use to describe central tendency for qualitative data? mean median mode weighted mean

mode

During a cold winter, the temperature stayed below zero for ten days (ranging from -20 to -5). The variance of the temperatures of the ten-day period is negative since all the numbers are negative cannot be computed since all the numbers are negative must be positive can be either negative or positive

must be positive

A recent survey of 200 small firms (annual revenue less than $10 million) asked whether an increase in the minimum wage would cause the firm to decrease capital spending. Possible responses to the survey question were: "Yes," "No," or "Don't Know." The scale of measurement for the data generated by this survey question is best classified as nterval ordinal nominal ratio

nominal

The covariance between the returns on two assets is negative. This occurs when on average, the return on one asset increases while the return on the other asset decreases the variance of one asset has a negative linear relationship with the variance of the other asset on average, the return on one asset decreases while the return on the other asset also decreases the standard deviation of one asset has a positive linear relationship with the standard deviation of the other asset

on average, the return on one asset increases while the return on the other asset decreases

The sum of the relative frequencies for all classes will always equal to the number of classes can be any value one the sample size

one

What kind of data assumes that the differences between categories are meaningless? ratio interval ordinal measured

ordinal

μ is an example of a population parameter mode sample statistic population variance

population parameter

Which of the following indicates the strongest relationship between two variables? r = 0.09 r = -0.6 r = 0.5 r = 2

r = -0.6

What is the scale of measurement of the distance between any two locations? Ordinal Interval Nominal Ratio

ratio

The diagram below is an example of a scatter plot illustrating a lack of correlation between tobacco and alcohol scatter plot illustrating a positive correlation between tobacco and alcohol scatter plot illustrating a perfect correlation between tobacco and alcohol histogram illustrating a positive correlation between tobacco and alcohol

scatter plot illustrating a positive correlation between tobacco and alcohol

The following graph shows the curb weight of seven cars, in pounds, along with their corresponding highway miles per gallon: This graph is an example of a line chart, and miles per gallon is the dependent variable in the graph scatter plot, and curb weight is the dependent variable in the graph line chart, and curb weight is the independent variable in the graph scatter plot, and miles per gallon is the dependent variable in the graph

scatter plot, and miles per gallon is the dependent variable in the graph

A smaller standard deviation for the normal probability distribution results in a fatter curve that is more spread out around the mean and not as tall skinnier curve that is more spread out around the mean and not as tall skinnier curve that is tighter and taller around the mean fatter curve that is tighter and taller around the mean

skinnier curve that is tighter and taller around the mean

Data that describe a characteristic about a sample is known as a population survey parameter statistic

statistic

If the variance of a data set is correctly computed with the formula using n - 1 in the denominator, which of the following is true? the data set could be either a sample or a population the data set includes all subjects of interest in the study the data set is a population the data set is a sample

the data set is a sample

For a continuous random variable x, the probability density function f(x) represents the probability at a given value of x the area under the curve at x the area under the curve to the right of x the height of the function at x

the height of the function at x

Which one of the following statements is true for a right-skewed distribution? The mean is roughly equal to the median. The mean is less than the median. The mean is greater than the mode. the mean is greater than the median.

the mean is greater than the median.

An analyst constructed the following frequency distribution on the monthly returns for 50 selected stocks: Class (in percent) Frequency -10 up to 0 8 0 up to 10 25 10 up to 20 15 20 up to 30 2 The frequency for the class "0 up to 10" is 25. This means that the number of stocks with returns of less than 10% is 25. the number of stocks with returns of 10% is 25. the percentage of stocks with returns between 0% and 10% is 25%. the number of stocks with returns between 0% and 10% is 25.

the number of stocks with returns between 0% and 10% is 25.

Which of the following characteristics does the interval scale NOT have? There is a true zero point. Numerical values are used to measure various characteristics. Values can be ranked. The differences between values are valid.

there is a true zero point

The data represents the stock price for Google at the end of the past four quarters. Which of the following types of data best describes these values? Time series Nominal Cross-sectional Ordinal

time series

A population is a larger data set than its corresponding sample.

true

Mathematical operations can be performed on ratio-scaled data.

true

The branch of statistical studies called descriptive statistics summarizes important aspects of a data set.

true

Which of the following symbols represents the mean of the sample? σ μ n x ¯

x ¯

Which of the following statements is NOT true concerning the attributes of z-scores? z-scores can be positive or negative for data values above the mean of the distribution z-scores are equal to zero for data values equal to the mean of the distribution z-scores are negative for data values below the mean of the distribution z-scores are positive for data values above the mean of the distribution

z-scores can be positive or negative for data values above the mean of the distribution

For an experiment in which a single die is rolled, the sample space is {1, 1, 3, 4, 5, 6} All suggested alternatives can be viewed as the sample space {1, 2, 3, 4, 4, 5} {2, 1, 3, 6, 5, 4}

{2, 1, 3, 6, 5, 4}

Consider the sample space of an experimental outcome denoting days of the week: S = {Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday}. Let's define an event: A = {Days when I have my stats classes} = {Tuesday, Thursday}. What is the complement of the event A? {Monday, Wednesday, Friday} {Tuesday, Thursday} {Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday} {Monday, Wednesday, Friday, Saturday, Sunday}

{Monday, Wednesday, Friday, Saturday, Sunday}

Consider two events: A = {apple pie, peach pie, pumpkin pie}; B = {cherry pie, blueberry pie, pumpkin pie}. The union of these events is {pumpkin pie} {apple pie, peach pie, pumpkin pie, cherry pie, blueberry pie} {apple pie, peach pie, cherry pie, blueberry pie} {apple pie, peach pie, pumpkin pie, cherry pie, blueberry pie, pumpkin pie}

{apple pie, peach pie, pumpkin pie, cherry pie, blueberry pie}

Consider two events: A = {apple pie, peach pie, pumpkin pie}; B = {cherry pie, blueberry pie, pumpkin pie}. The intersection of these events is {apple pie, peach pie, pumpkin pie, cherry pie, blueberry pie, pumpkin pie} {apple pie, peach pie, cherry pie, blueberry pie} {pumpkin pie} {apple pie, peach pie, pumpkin pie, cherry pie, blueberry pie}

{pumpkin pie}

The following table shows the probability distribution for the number of boats sold daily at Boats Unlimited. What is the probability that exactly 3 boats are sold? x f(x) 0 0.20 1 0.30 2 0.32 3 ? 4 0.05 5 0.02 Can be any value between 0 and 1 0.62 0.11 Need to know the distribution function to calculate the probability

.11

If P(A) = 0.79, find P(A'). 0.105 0.21 0.395 0.79

.21

Consider the following frequency distribution: Class Frequency 12 up to 15 3 15 up to 18 6 18 up to 21 3 21 up to 24 4 24 up to 27 4 What is the relative frequency of the class "15 up to 18"? 0.3 0.2 0.25 0.35

.3

For the standard normal probability distribution, the area under the probability density function to the left of the mean is 0.5 any value between 0 to 1 1 Cannot say exactly without knowing the value of the mean

.5

Consider the following frequency distribution: Class Frequency 12 up to 15 3 15 up to 18 6 18 up to 21 3 21 up to 24 4 24 up to 27 4 What is the cumulative relative frequency of the class "18 up to 21"? 0.9 0.6 0.3 1.00

.6

For any continuous random variable, the probability that the random variable takes on exactly a specific value is 0.5 1 any value between 0 to 1 0

0

Consider the following probability distribution for the random variable x. xP(x)-20.2-10.100.310.4 The expected value of this random variable is: 1 0.1 -0.1 -1

-.1

The covariance between the returns of stocks A and B is -0.112. The standard deviation of the rates of return is 0.26 for stock A and 0.81 for stock B. The correlation of the rates of return between A and B is the closest to -2.52 -0.53 -0.24 0.53

-.53

A survey of adults who typically work full-time from home recorded their current education levels. The results are shown in the table below: Education LevelFrequencyBachelor's degree or higher37Some college13High school diploma only7Less than high school diploma3 The probability that a randomly selected adult who works from home has less than a high school diploma is 0.2 0.05 0.02 0.17

.05