BUAL 2600 Final Study Guide

The random variable x has a uniform distribution when x lies between the values of 4 and 10. When x = 10, what is the value of f(x)?

0

If the sampled population has a mean of 48 and standard deviation of 16, then respectively the mean and the standard deviation for the sampling distribution of x¯ for n = 16 are

48 4

Pie Chart

A circle divided into slices where the size of each slice represents its relative frequency or percent frequency

Ogive

A line graph that depicts cumulative frequencies

Ordinal

A qualitative variable for which there is a meaningful ordering, or ranking, of the categories Example: teaching effectiveness

Nominative

A qualitative variable for which there is no meaningful ordering, or ranking, of the categories Example: gender, car color

Population

A set of all elements about which we wish to draw conclusions

Sample

A subset of the elements of a population

The measurement in a sample or a population that occurs most frequently is the ________. A) mode B) mean C) median D) outlier E) average

A) mode

Interval

All of the characteristics of ordinal plus. Measurements are on a numerical scale with an arbitrary zero point. Can only meaningfully compare values by the interval between them Example: temperature

Ratio

All the characteristics of interval plus. Measurements are on a numerical scale with a meaningful zero point. Zero means "none" or "nothing"

If n = 15 and p = .4, then the standard deviation of the binomial distribution is _______. A) 9 B) 6 C) 3.6 D) 1.897

B) 6

If two events are independent, we can ________ their probabilities to determine the intersection probability. A) divide B) add C) multiply D) subtract

B) add

Which of the following is not a discrete random variable? A) the number of times a light changes red in a 10-minute cycle B) the number of minutes required to run 1 mile C) the number of defects in a sample selected from a population of 100 products D) the number of criminals found in a five-mile radius of a neighborhood

B) the number of minutes required to run 1 mile

A standard normal distribution has a mean of ________ and standard deviation of ________. A) zero, zero B) zero, one C) one, one D) one, zero

B) zero, one

A normal population has 99.73 percent of the population measurements within ________ standard deviation(s) of the mean. A) 1 B) 2 C) 3 D) 4

C) 3

________ can be used to study the relationship between two variables.

Cross-Tabulation Tables

Which of the following is a type of question used in survey research?A) dichotomous B) open-ended C) multiple-choice D) All of the other answers are correct.

D) All of the other answers are correct.

Which of the following is a categorical variable? A) air temperature B) bank account balance C) daily sales in a store D) whether a person has a traffic violation E) value of company stock

D) whether a person has a traffic violation

Cross-Sectional Data

Data collected at the same or approximately the same point in time

Cumulative Distributions

Distributions that add up and must be paid once a corporation has funds to do so

A quantitative variable can also be referred to as a categorical variable.

False

In a data set of information on college business students, an example of an element is their cumulative GPA.

False

The number of sick days taken by employees in 2008 for the top 10 technology companies is an example of time series data.

False, Cross-Sectional data

Daily high temperature in a local community collected over a 30-day time period is an example of cross-sectional data.

False, Time-Series data

Empirical Rule

If a population has mean μ and standard deviation σ and is described by a normal curve, then - 68.26% of the population measurements lie within one standard deviation of the mean: [μ‐σ, μ+σ] - 95.44% lie within two standard deviations of the mean: [μ-2σ, μ+2σ] - 99.73% lie within three standard deviations of the mean: [μ-3σ, μ+3σ]

Statistical ________ refers to using a sample of measurements and making generalizations about the important aspects of a population.

Interference

The ________ of two events A and B is the event that consists of the sample space outcomes belonging to both event A and event B.

Intersection

Chebyshev's Theorem

Let μ and σ be a population's mean and standard deviation, then for any value k > 1 At least 100(1 - 1/k2)% of the population measurements lie in the interval [μ-kσ, μ+kσ] Only practical for a non-mound-shaped population that is not very skewed

A(n) ________ is a graph of a cumulative distribution.

Ogive

An identification of police officers by rank would represent a(n) ________ level of measurement.

Ordinal

If P(A) > 0 and P(B) > 0 and events A and B are independent, then ________.

P(A|B) = P(A)

All of the following are used to describe quantitative data except the ________.

Pie Chart

Frequency Polygons

Plot a point above each class midpoint at a height equal to the frequency of the class Useful when comparing two or more distributions

Which of the following distributions can be used to solve the following problem?The average number of cars arriving at a drive-through fast-food restaurant is 3 cars in 10 minutes. What is the probability that exactly four cars will arrive in a 5-minute interval?

Poisson

________ says that if the sample size is sufficiently large, then the sample means are approximately normally distributed.

The Central Limit Theorem

Variance

The average of the squared deviations of all the population measurements from the population mean

box and whisker plot

The box plots the: First quartile, Q1 Median, Md Third quartile, Q3 Determine the values of lower and upper limits: Located 1.5 * IQR away from the quartiles: Q1 ± (1.5 * IQR) Draw one whisker from Q1 to the smallest value that is between the lower and upper limits. Draw the other whisker from Q3 to the largest value that is between the lower and upper limits. Plot each outlier

Random Sampling

The key technique employed by survey researchers, which operates on the principle that everyone should have an equal probability of being selected for the sample.

Skewed to the Left

The left tail of the histogram is longer than the right tail

In which of the following are the two events A and B always independent?

The probability of event A is not influenced by whether event B occurs, or P(A|B) = P(A).

Symmetrical

The right and left tails of the histogram appear to be mirror images of each other

Skewed to the Right

The right tail of the histogram is longer than the left tail

Standard Deviation

The square root of the population variance

Qualitative (categorical)

the possible measurements fall into several categories

Quantitative

the possible measurements of the values of a variable are numbers that represent quantities

Variable

any characteristic of an element

A ________ displays the frequency of each class with qualitative data and a ________ displays the frequency of each class with quantitative data.

bar chart, histogram

The grade a student received on an examination was transformed to a z value, which was negative. Therefore, we know that he scored

below the mean

The requirement that the probability of success remains constant from trial to trial is a property of the ________ distribution.

binomial

A(n) ________ is the probability that one event will occur given that we know that another event already has occurred.

conditional probability

Tiime-Series Data

data collected over different time periods

A stem-and-leaf display is best used to ________.

display the shape of the distribution

Multistage Cluster Sampling

divide population into clusters and then randomly select clusters to sample

Stratified Random Sampling

divide population into non-overlapping groups (strata) then select a random sample from each strata

Data

facts and figures from which conclusions can be drawn

Whenever the population has a normal distribution, the sampling distribution of x¯ is a normal or near normal distribution

for any sample size.

The area under the normal curve between z = 0 and z = 1 is ________ the area under the normal curve between z = 1 and z = 2.

greater than

As the sample size ________, the variation of the sampling distribution of x¯ ________.

increases; decreases

Systematic Sampling

list population, select random starting point, sample each nth element

Outliers

measurements that are very different from other measurements

Events that have no sample space outcomes in common, and therefore cannot occur simultaneously, are ________.

mutually exclusive

The mean of the binomial distribution is equal to

n*p

The population of all sample proportions has a normal distribution if the sample size (n) is sufficiently large. The rule of thumb for ensuring that n is sufficiently large is

np ≥ 5 and n(1 − p) ≥ 5.

The ________ of an event is a number that measures the likelihood that an event will occur when an experiment is carried out.

probability

Judgement Sampling

samples in which a person who is extremely knowledgeable about the population selects population elements he or she feels are most representative

Voluntary Sampling

samples in which participants self-select

Probabiliity sampling

sampling where we know the chance that each element in the population will be included in the sample

Convenience Sampling

sampling where we select elements because they are convenient to sample

Data Set

the data that are collected for a particular study