Final Exam
Decide whether the random variable x is discrete or continuous. Explain your reasoning. Let x represent the time it takes to run a mile.
Continuous, because x is a random variable that cannot be counted.
Determine whether the underlined numerical value is a parameter or a statistic. Explain your reasoning. The average grade on the midterm exam in a certain math class of 50 students was an 88 <--
Parameter, because the data set of all 50 midterm exams in the math class is a population.
What technology format could be used to generate ten random numbers between 1 and 950?
RandInt(1,950,10)
Determine whether the data set is a population or a sample. Explain your reasoning. 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.
Poisson Distribution
1. The xperiment consists of counting the number of times x an event occurs in a given interval.The interval can be an interval of time, area, or volume. 2. The probability of the event occuring is the same for each interval.. 3. The number of occurrences in one interval is independent of the number of of occurrences in other intervals. The probability of exactly x occurrences in an interval is P(x) = µ^x *e^-µ / x!
Geometric Distribution (Conditions)
1. Trial is repeated until success. 2. Repeated trials are independent of the other. 3. The probability of success P is the same for reach trial. 4. The random variable x represents the number of the trial in which success occurs. P(x) =pq^ x-1
Frequency Distribution, when is it skewed left?
A frequency distribution is skewed left when a tail of the graph elongates more to the left than to the right
Frequency Distribution, when is it skeweed right?
A frequency distribution is skewed right when its tail extends to the right instead of to the left.
Frequency Distribution, when is it symmetric?
A frequency distribution is symmetric when a vertical line can be drawn through the middle of a graph of the distribution and the resulting halves are approximately mirror images.
Frequency Distribution, when is it uniform?
A frequency distribution is uniform when all entries, or classes, in the distribution have equal or approximately equal frequencies
What is the difference between a frequency polygon and an ogive
A frequency polygon displays class frequencies while an ogive displays cumulative frequencies.
What is the difference between a frequency polygon and an ogive?
A frequency polygon displays class frequencies while an ogive displays cumulative frequencies.
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
Simple random
A sample in which every possible sample of the same size has the same chance of being selected from a population.
How is a sample related to a population?
A sample is a subset of a population.
The following appear on a physician's intake form. Identify the level of measurement of the data. A)Family history of illness B)Happiness level scale of 0 to 10 C) Height D)Temperature
A) Nominal B)Ordinal C)Ratio D) Interval
Use the Empirical Rule. The mean speed of a sample of vehicles along a stretch of highway is 63 miles per hour, with a standard deviation of 4 miles per hour. Estimate the percent of vehicles whose speeds are between 59 miles per hour and 67 miles per hour. (Assume the data set has a bell-shaped distribution.)
Approximately 68% of vehicles travel between 59 miles per hour and 67 miles per hour.
law of large numbers
As an experiment is repeated over and over, the empirical probability of an event approaches the theoretical (actual) probability of the event.
About 90% of babies born with a certain ailment recover fully. A hospital is caring for seven babies born with this ailment. The random variable represents the number of babies that recover fully. Decide whether the experiment is a binomial experiment. If it is, identify a success, specify the values of n, p, and q, and list the possible values of the random variable x.
Binomial experiment Success = baby recovers. n = 7, p =.90 x = 0,1,2,....7
What is a similarity between the Empirical Rule and Chebychev's Theorem?
Both estimate proportions of the data contained within k standard deviations of the mean. Bo
In terms of displaying data, how is a stem-and-leaf plot similar to a dot plot?
Both plots can be used to determine specific data entries. Both plots can be used to identify unusual data values. Both plots show how data are distributed.
After a hurricane, a disaster area is divided into 200 equal grids. Forty 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 is the potential bias?
Certain grids may have been much more severely damaged than others. The grids that are selected may not be representative in terms of damage. Certain grids may have been much more severely damaged than others. Severely damaged grids may have fewer occupied households.
What is the difference between class limits and class boundaries?
Class limits are the least and greatest numbers that can belong to the class. Class boundaries are the numbers that separate classes without forming gaps between them. For integer data, the corresponding class limits and class boundaries differ by 0.5.
After a hurricane, a disaster area is divided into 200 equal grids. Forty 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 an athletic facility, a researcher asks 363 students about their dating habits. What type of sampling is this?
Convenience sampling is used, because students are chosen due to convenience of location.
Systematic
Each member of a population is assigned a number. The members of the population are ordered in some way, a starting number randomly selected, and then sample members are selected at regular intervals from starting number.
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.
True or False. A statistic is a measure that describes a population characteristic
False. A statistic is a measure that describes a sample characteristic.
In a frequency distribution, the class width is the distance between the lower and upper limits of a class. T/F
False. In a frequency distribution, the class width is the distance between the lower or upper limits of consecutive classes.
T/F 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.
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.
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.
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
After constructing a relative frequency distribution summarizing IQ scores of college students, what should be the sum of the relative frequencies?
If percentages are used, the sum should be 100%. If proportions are used, the sum should be 1.
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.
Percentile explaination
If your 3-month-old daughter is in the 40th percentile for weight, that means 40 percent of 3-month-old girls weigh the same as or less than your baby, and 60 percent weigh more. The higher the percentile number, the bigger your baby is compared to other babies her same age.
A state lottery randomly chooses 8 balls numbered from 1 through 36 without replacement. You choose 8 numbers and purchase a lottery ticket. The random variable represents the number of matches on your ticket to the numbers drawn in the lottery. Determine whether this experiment is binomial. If so, identify a success, specify the values n, p, and q and list the possible values of the random variable x.
Is the experiment binomial? No, because the probability of success is different for each trial.
What are some benefits of using graphs of frequency distributions?
It can be easier to identify patterns of a data set by looking at a graph of the frequency distribution
What are some benefits of using graphs of frequency distributions?
It can be easier to identify patterns of a data set by looking at a graph of the frequency distribution.
Stratified
Members of a population are divided into two or more subsets, called strata, that share a similar characteristics. A sample is then randomly selected from each of the strata. Using a stratified sample ensures that each segment of the population is represented.
The class levels of 31 students in a physics course are shown below. Find the mean, median, and mode of the data, if possible. If any measure cannot be found, explain why. Freshman: 6 Junior: 10 Sophomore: 12 Senior: 3
No median or mean. Data is nominal. Mode is sophomore. Typical data entry.
Can two events with nonzero probabilities be both independent and mutually exclusive?
No, two events with nonzero probabilities cannot be independent and mutually exclusive because if two events are mutually exclusive, then when one of them occurs, the probability of the other must be zero.
independent event (probability)
Occurrence of one event does not affect subsequent events P(B|A) = P(B) or P(A|B)=P(A).
What levels of measurement can data be quantitative?
Ordinal, Ratio, Interval
Continous Probability Distribution
Probability distribution for continuous random variables on an infinite number line.
The regions of a country with the six highest per capita incomes last year are shown below. 1. Northeast 2. Eastern 3. Southeast 4. Western 5. Southwest 6. Northwest Determine whether the data are qualitative or quantitative and identify the data set's level of measurement.
Qualitative. Ordinal.
Describe the relationship between quartiles and percentiles.
Quartiles are special cases of percentiles. Q1 is the 25th percentile, Q2 is the 50th percentile, and Q3 is the 75th percentile.
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.
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 the value is a parameter or a statistic. A study of 6,076 adults in public rest rooms found that Modifying 23 % with underline did not wash their hands before exiting.
Statistic
Determine whether the given value is a statistic or a parameter. Upper A sample of professors is selected and it is found that 55 % own a vehicle.
Statistic because the value is a numerical measurement describing a characteristic of a sample.
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 is $ 54000
Statistic, because the data set of salaries of 50 employees is 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.
The following appear on a physician's intake form. Identify the level of measurement of the data. Temperature Age Allergies Change in health left scale of - 5 to 5
Temperature: interval Age: Ratio Allergies: nominal Change in health: Ordinal.
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
If a z-score is zero, which of the following must be true? Explain your reasoning. bullet The mean is zero. bullet The corresponding x-value is zero. bullet The corresponding x-value is equal to the mean.
The corresponding x-value is equal to the mean, because the z-score is equal to the difference between the x-value and the mean, divided by the standard deviation.
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. a) Identify the experimental units and treatments used in this experiment.
The experimental units are theTh 30- to 35-year-old females being given the treatment. The treatment is the new allergy drug.
Cluster sample
The population is divided into subgroups, called clusters, and all of the members of one or more (but not all) clusters are selected.
Statified Sampling
The population is divided into subgroups, called strata, based on some characteristic, and then a random sample is taken from each stratum
Range of probabilities rule
The probability of an event E is between 0 and 1 0 ≤ P(E) ≤ 1
Determine whether the random variable x is discrete or continuous. Explain. Let x represent the distance a baseball travels in the air after being hit.
The random variable is continuous, because it has an uncountable number of possible outcomes.
Empirical Rule
The rules gives the approximate % of observations w/in 1 standard deviation (68%), 2 standard deviations (95%) and 3 standard deviations (99.7%) of the mean when the histogram is well approx. by a normal curve 68 - 95 - 99.7
Questioning students as they leave an athletic facility, a researcher asks 363 students about their dating habits What potential sources of bias are present, if any? Select all that apply.
The sample only consists of members of the population that are easy to get. These members may not be representative of the population. Because of the personal nature of the question, students may not answer honestly.
Identify the sample space of the probability experiment and determine the number of outcomes in the sample space. Playing the game of roulette, where the wheel consists slots numbered 00, 0, 1, 2, ..., 43 To play the game, a metal ball is spun around the wheel and is allowed to fall into one of the numbered slots. Identify the sample space.
The sample space is {00, 0, 1, 2, ..., 43}. 45 outcomes. Starts at 00.
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.
True or False A sample statistic will not change from sample to sample
The statement is false. A sample statistic can change from sample to sample.
T/F 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 statement below is true or false. If it is false, rewrite it as a true statement. A combination is an ordered arrangement of objects.
The statement is false. A true statement would be "A permutation is an ordered arrangement of objects."
T/F Some quantitative data sets do not have medians.
The statement is false. All quantitative data set have medians
An ogive is a graph that displays relative frequencies. T/F
The statement is false. An ogive is a graph that displays cumulative frequencies.
A double-blind experiment is used to increase the placebo effect.
The statement is false. Double blinding is used to decrease the placebo effect
The 50th percentile is equivalent to Upper Q 1
The statement is false. The 50th percentile is equivalent to Upper Q 2.
A student's IQ score is in the 91st percentile on an intelligence scale. Make an observation about the student's IQ score
The student has a higher IQ score thanTh 91% of the students in the same age group
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 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
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 the study is an observational study or an experiment. Explain. In a survey of 1291 adults in a country, 54% said the country's leader should release all medical information that might affect their ability to serve.
The study is observational, because it does not apply a treatment to the adults.
(c) How could this experiment be designed to be a double-blind? Choose the correct answer below.
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.
Draw two normal curves that have the same mean but different standard deviations. Describe the similarities and differences.
The two curves will have the same line of symmetry. The curve with the larger standard deviation will be more spread out than the curve with the smaller standard deviation.
For the given pair of events, classify the two events as independent or dependent. Driving 30 mph over the speed limit Getting a speeding ticket
The two events are dependent because the occurrence of one affects the probability of the occurrence of the other.
For the given pair of events, classify the two events as independent or dependent. Winning $ 100 on your first trip to the casino Winning $ 100 on your second trip to the casino
The two events are independent because the occurrence of one does not affect the probability of the occurrence of the other.
Why is the standard deviation used more frequently than the variance?
The units of variance are squared. Its units are meaningless.
Qualitative or quantitative? Species of fish in a lake?
The variable is qualitative because species are attributes or labels.
qualitative or quantitative. Distances between plants
The variable is quantitative because distances are numerical measurements.
Qualitative or quantitative? Favorite color
The variable is Th qualitative because color describes an attribute or characteristic.
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. (b) Identify a potential problem with the experiment design being used and suggest a way to improve it.
There may be a bias on the part of the researcher if the researcher knows which patients were given the real drug.
Quartiles
Three values represented by Q1, Q2, and Q3 that divide the distribution into four subsets. About one - half of the data falls on or below Q2 (the second quartile is the median). About 3/4 of data fall on or below Q3.
It is impossible for the Census Bureau to obtain all the census data about the population of the United States.
True
T/F A data set can have the same mean, median, and mode.
True
T/F Class boundaries ensure that consecutive bars of a histogram touch.
True
T/F The midpoint of a class is the sum of its lower and upper limits divided by two.
True
T/F When each data class has the same frequency, the distribution is symmetric.
True
T/F Class boundaries ensure that consecutive bars of a histogram touch.
True
The number of different ordered arrangements of n distinct objects is n!.
True
The second quartile is the median of an ordered data set.
True
When an event is almost certain to happen, its complement will be an unusual event
True
The midpoint of a class is the sum of its lower and upper limits divided by two.
True. midpoint = (lower class limit) + (upper class limit) / 2
mutually exclusive
Two events that cannot occur at the same time
The mean value of land and buildings per acre from a sample of farms is $1200, with a standard deviation of $100. The data set has a bell-shaped distribution. Using the empirical rule, determine which of the following farms, whose land and building values per acre are given, are unusual (more than two standard deviations from the mean). Are any of the data values very unusual (more than three standard deviations from the mean)? $1034 $1445 $1043 $844 $1280 $1348
Which of the farms are unusual (more than two standard deviations from the mean)? 1445 844 Which of the farms are very unusual (more than three standard deviations from the mean)? 844
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.
normal distribution
a continuous probability distribution for a random variable x. The graph of a normal distribution is called the normal curve. It has these properties. 1. The mean, median and mode are equal. 2. The normal curve is bell-shaped and symmetric about the mean. 3. The total area under the normal curve is equal to 1. 4. The normal curve approaches, but never touches, the x-axis as it extends farther and farther away from the mean. 5. Between µ - sigma and µ + sigma (in the center of the curve), the graph curves downward. The graph curves upward to the left of µ - sigma and to the right of µ + sigma. The points at which the curve changes from curving upward to downward are called inflection points.
binomial experiment
a probability experiment that satisfies these conditions. 1. Experiment has a fixed number of trails, where each trial is independent of other trials. 2. There are only tow possible outcomes of interest for each trial. Each out come is classified as success or failure. 3. The probability of a success is the same for reach trial. 4. The random variable x counts the number of successful trails.
probability density function
a probablity density function has two requirements: 1) the total area under the curve is equal to 1 2) the function can never be negative
discrete
a random variable is discrete when it has finite or countable number of possible outcomes
Random:
a sample in which every member of a population has an equal chance of being selected.
simple random sample
a sample in which every possible sample of the same size has the same chance of being selected.
event
a subset of the sample space.
frequency distribution
a table that shows classes or intervals of data entries with a count of the number of entries in each class
multiplication rule
the probability that two or more independent events will occur together is the product of their individual probabilities P(A and B) = P(A) x P(B|A) Dependent. P(A and B) = P(A) x P(B) Independent.
outcome
the result of a single trial in a probability experiment
complement of event E
the set of all outcomes in a sample space that are not included in event E
sample space
the set of all possible outcomes of a probability experiment
midpoint of a class
the sum of the lower and upper limits of the class divided by 2. sometimes called the class mark.
Why is it correct to say "a" normal distribution and "the" standard normal distribution? Describe the cases in which the different terms are used. Choose the correct answer below.
"The" standard normal distribution is used to describe one specific normal distribution left parenthesis mu equals 0 comma sigma equals 1 right parenthesis . "A" normal distribution is used to describe a normal distribution with any mean and standard deviation.
The Empirical Rule
(or 68-95-99.7 Rule) indicates percentages of data that lie within one, two, and three standard deviations of the mean for data sets with distributions that are approximately symmetric and bell-shaped. Assumes approx symmetric and bell shaped.
lower and upper class limits
-smallest value within the class -largest value within the class
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.
What is the total area under the normal curve?
1
Steps to calculate midpoint
1) Add lower and upper limits together 2) Divide by 2
Steps for Relative frequency
1) Add the sample size/frequencies together. 2) Divide individual frequency by the total amount. This should be a decimal/percentage
Match the frequency distribution of 180 rolls of a dodecahedron (a 12-sided die) with one of the histograms shown below. (steps)
1)What are the possible outcomes: 12 2) Are any outcomes more likely than the other?: No. 3) Therefore, the graph should be uniform
Identify the sample space of the probability experiment and determine the number of outcomes in the sample space. Randomly choosing an even number between 1 and 10 comma inclusive
2,4,6,8,10 There are 5 outcomes
Determine which numbers could NOT be used to represent the probability of an event.
64/25 because probabilities cannot be greater than 1. -1.5 because probability cannot be less than 0.
Explain how to use random number assignment Use the row of numbers to generate 12 random numbers between 01-99 78086 85201 etc
99 is a two digit number. Break up the numbers in twos: 78 | 08 | 68 | 52 | 01 | Numbers that start with zero are singular. Numbers that end with a single digit pick up the second digit from the next number.
expected value
= E(x) = µ = Σx ⋅ P(x) The expected value of a discrete random variable is equal to the mean of the random variable. Represents the break-even point in profit and loss analysis. Can be negative.
Is it a simple event? tossing heads and rolling a 3
A = {H3} Event A has one outcome, it is simple
What is the difference between a census and a sampling?
A census includes the entire population. A sampling includes only part of the population
Steps for determining level of measurement
Ask if you can: 1) Put the data into categories? 2) Can the data be arranged in order? 3) Can one label value be subtracted from another? 4) Can one label value be considered a multiple of another?
Is it simple? Tossing heads and rolling an even number
B = {H2, H4, H6} Event B has more than one outcome, so it is not simple.
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. The Empirical Rule assumes the distribution is approximately symmetric and bell-shaped and Chebychev's Theorem makes no assumptions.
What are the two main branches of statistics?
Descriptive and inferential
You randomly select one card from a standard deck of 52 playing cards. Event C is selecting a club. nothing
Event C has 13 outcomes. (There are 13 clubs in a deck of cards) Not a simple event, more than one outcome
Chebychev's Theorem
Gives a rule for the portion of any data set lying within k standard deviations (k > 1) of the mean. Does not assume symmetric or bell shaped.
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.
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 1965, researchers used random digit dialing to call 1200 people and ask what obstacles kept them from voting. What potential sources of bias were present, if any? Select all that apply.
Individuals may have refused to participate in the sample. This may have made the sample less representative of the 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. 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.
Why is a sample used more often than a population?
It is usually impossible to count the entire population
In a normal distribution, which is greater, the mean or the median? Explain.
Neither; in a normal distribution, the mean and median are equal
What levels of measurement can be qualitative?
Nominal, Ordinal
The top five books on the best seller list last year are shown below. 1. The Racketeer 2. Gone Girl 3. Spring Fever 4. Threat Vector 5. Private London Identify the level of measurement of the data set. Explain your reasoning
Ordinal. The data can be arranged in order comma but the differences between data entries are not meaningful.
What are some benefits of representing data sets using frequency distributions?
Organizing the data into a frequency distribution can make patterns within the data more evident.
What are some benefits of representing data sets using frequency distributions? What are some benefits of using graphs of frequency distributions?
Organizing the data into a frequency distribution can make patterns within the data more evident.
independent or dependent? Selecting a king from a standard deck of 52 cards, not replacing it and then selecting a queen.
P(B) = 4/52 and P(B|A) = 4/51. Occurrence of A changes B so events are dependent.
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.
Determine whether the data set is a population or a sample. Explain your reasoning. The number of floors in each home in a town.
Population, because it is a collection of the number of floors for all homes in the town.
The heights in inches right parenthesis of a sample of a species of tree two years after being planted are shown below. 25.6 22.6 25.5 23.3 22.4 21.6 25.7 25.5 24.3 Determine the level of measurement of the data set. Explain your reasoning.
Ratio. The data can be ordered and differences between data entries are meaningful, and a zero entry is an inherent zero.
Determine whether the data set is a population or a sample. Explain your reasoning. The number of cars for 10 households in a neighborhood of 30 households
Sample, because the collection of the number of cars for 10 households is a subset of all households in the neighborhood.
In 1965, researchers used random digit dialing to call 1200 people and ask what obstacles kept them from voting.
Simple random sampling was used, since each number had an equal chance of being dialed, so all samples of 1200 phone numbers had an equal chance of being selected.
In 1965, researchers used random digit dialing to call 1400 people and ask what obstacles kept them from exercising. What type of sampling was used? What potential sources of bias were present, if any? Select all that apply.
Simple random sampling was used, since each number had an equal chance of being dialed, so all samples of 1400 phone numbers had an equal chance of being selected. 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 refused to participate in the sample. This may have made the sample less representative of the 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.
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 greater than Q3 + 1.5 ( IQR right) or less than Q1 -1.5 (IQR) are considered outliers.
What requirements are necessary for a normal probability distribution to be a standard normal probability distribution?
The mean and standard deviation have the values of mu equals 0 and sigma equals 1.
Determine whether the number describes a population parameter or a sample statistic. Explain your reasoning. Sixty-three of the 97 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.
You toss a fair coin nine times and it lands tails up each time. The probability it will land heads up on the tenth flip is greater than 0.5.
The statement is false. The correct statement is "You toss a fair coin nine times and it lands tails up each time. The probability it will land heads up on the tenth flip is exactly 0.5."
The mean is the measure of central tendency most likely to be affected by an outlier.
The statement is true
Determine whether the following events are mutually exclusive. Explain your reasoning. Event A: Randomly select a female economics major. Event B: Randomly select a economics major who is 20 years old
These events are not mutually exclusive, since it is possible to select a female economics major who is 20 years old.
Determine whether the following events are mutually exclusive. Explain your reasoning. Event A: Randomly select a voter who legally voted for the President in South Carolina. Event B: Randomly select a voter who legally voted for the President in California.
These events are mutually exclusive, since it is not possible for a voter to both legally vote for a president in south carolina and have legally voted in California.
A motorcycle's fuel efficiency represents the ninth decile of vehicles in its class. Make an observation about the motorcycle's fuel efficiency.
The motorcycle's fuel efficiency is greater than the fuel efficiency for 90% of vehicles in its class
Every thirtieth 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.
Type of sampling: Systematic sampling is used, because every thirtieth person is selected Bias: The wording of the question may direct respondents towards a particular author. If there is a regular pattern to the people entering the library, the sample may not be representative
continious variable
Variable where there is an uncountable number of possible outcomes, represented by an interval on a number line.
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 nminus1, then the square root of the result is taken.
Given a data set, how do you know whether to calculate sigma 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 sigma is calculated. If the data are a sample, then s is calculated.
frequency histogram
a bar graph that represents the frequency distribution of a data set. 1. The horizontal scale is quantitative and mesures data entries. 2. The vertical scale measures the frequencies of the classes. 3. Consecutive bars much touch.
probablity experiment
an action, or trail, through which specific results (counts, measurements, or responses) are obtained.
deviation of an entry
an entry, x, in a population data set is the difference between the entry and the mean of the data set. x = x - µ
simple event
an event that consists of a single outcome
class boundaries
are the numbers that separate classes without forming gaps between them. for data that are integres, subtract. 5 from each lower limit to find the lower class boundaries. to find the upper class boundaries add .5 to each upper limit. the upper boundary of a class will equal the lower boundary of the next higher class.
rang
difference between the max and minimum data entries
x represents the number of dependent children in a household. Is the random variable x discrete or continuous?
discrete
class width
distance between lower(or upper) limits of consecutive classes
systematic sample
each member of the population is assigned a number; the population is ordered using these numbers, a starting number is randomly selected, and then sample members are selected at regular intervals from the starting number.
frequency polygon
graph of a frequency distribution that shows the number of instances of obtained scores, usually with the data points connect by straight lines. emphasizes the continuous change in frequencies.
Fundamental Counting Principle
if one event can occur in m ways and a second event can occur in n ways, then the number of ways the two events can occur in sequence is m x n. This rule can be extended to any number of events occuring in sequence.
Fractiles
numbers that partition, or divide, an order data set into equal parts.
Parameter
numerical summary of a population
convenience sample
only members of the population that are easy to get are sampled.
In a poll, 1 comma 005 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, 46% said that they were in favor. Identify the population and the sample.
population: all men Sample: 1005 men selected
random variable x
represents a value associated with each outcome of a probability experiment.
standard score (z-score)
represents the number of standard deviations a value x lies from the mean, μ. To find the z score for a value use the formula z = value - mean --------------- standard deviation = x- μ --------- σ
subjective probability
result from intuition, educated guesses, and estimates
A study found that people who suffer from obstructive sleep apnea are at increased risk of having heart disease. Identify the two events described in the study. Do the results indicate that the events are independent or dependent?
sleep apnea and heart disease. dependent.
population variance
the average of the squares of the deviations population variance = σ^2 =Σ(x - μ)^2 ------------ N
standard deviation
the population data set of N entries is the square root of the population variance. σ= √σ^2
Cluster
the population is divided into groups (or clusters) and all of the members in one or more (but not all) of the clusters are selcted. To avoid a biased sample, care must be taken to ensure that all clusters have similiar characteristics.
relative frequency of a class
the portion or percentage of the data that falls in that class. divide the frequency f by the same size.
Conditional Probability
the probability of an event ( A ), given that another ( B ) has already occurred. Denoted by P (B|A) Read as probability of B given A.
Determine whether the statement below is true or false. If it is false, rewrite it as a true statement. When you divide the number of permutations of 11 objects taken 3 at a time by 3!, you will get the number of combinations of 11 objects taken 3 at a time.
true
classical (or theoretical) probability
used when each outcome in a sample space is likely to occur. The classical probability for an event E is given by: P(E) = Number of outcomes in event E -------------- Total number of outcomes in sample space
tree diagram
visual display of the outcomes of a probability experiment by using branches that originate from a starting point.