Business Modeling Exam 1
The standard normal distribution has a mean and a standard deviation respectively equal to a. 0 and 0. b. 1 and 1. c. 1 and 0. d. 0 and 1.
0 and 1.
If events A and B are mutually exclusive, then the probability of both events occurring simultaneously is equal to a. 0.0. b. 0.5. c. 1.0. d. any value between 0.5 and 1.0.
0.0.
If A and B are any two events with P(A) = 0.8 and P(B|) = 0.7, then P(and B) is a. 0.56. b. 0.14. c. 0.24. d. none of these choices.
0.56
The probability of an event and the probability of its complement always sum to a. 1. b. 0. c. any value between 0 and 1. d. any positive value.
1
Without performing any calculations, which of the following data sets has the greatest sample standard deviation? a. 1,2,3,4,5,6 b. 1,1,3,5,5,6 c. 3,3,3,3,3 d. 1,1,1,5,5,5 e. 1,1,3,3,6,6
1,1,1,5,5,5
If we plot a continuous probability distribution f(x), the total probability under the curve is 1. If we plot a continuous probability distribution f(x), the total probability under the curve is a. -1. b. 0. c. 1. d. 100.
1.
If two events are collectively exhaustive, what is the probability that one or the other occurs? a. 0.25 b. 0.50 c. 1.00 d. This cannot be determined from the information given.
1.00
1. If A and B are any two events with P(A) = 0.8 and P(B|A) = 0.4, then the joint probability of A and B is: a. 0.80 b. 0.40 c. 0.32 d. 1.20
1.20
Suppose that a histogram of a data set is approximately symmetric and "bell shaped". Approximately percent of the observations are within three standard deviation of the mean.
99.7%
One-tailed alternative hypotheses use the _____ symbol. a. ≠ b. < or > c. = d. <_ or _>
<_ or _>
The decision-making themes covered in Business Analytics: Data Analysis & Decision Making include which of the following? a. Optimization techniques b. Decision analysis with uncertainty c.Structured sensitivity analysis d. All of these choices
All of these choices
Which of the following are reasons for why simple random sampling is used infrequently in real applications? a. Samples can be spread over a large geographic region. b. Simple random sampling requires that all sampling units be identified prior to sampling. c. Simple random sampling can result in underrepresentation or overrepresentation of certain segments of the population. d. All of these choices are valid reasons.
All of these choices are valid reasons.
Which sign is possible in an alternative hypothesis? a. > b. < c. ≠ d. All of these signs are possible
All of these signs are possible
Which of the following is true? a. When entering an expression of text into an excel function, it must be enclosed in double quotes. b. A spreadsheet model should always include input numbers, rather than cell references, in formulas. c. If we enter A1:A5 as part of an Excel function, this refers to cells A2, A3, and A4...the cells that are between A1 and A5, exclusive. d. All of these statements are true.
All of these statements are true.
Which of the following statements are true? a. Three important themes run through the book: data analysis, decision making, and uncertainty. b. Data analysis includes data description, data inference, and the searching for relationships in data c. Decision making includes optimization techniques for problems with no uncertainty, decision analysis for problems with uncertainty, and structured sensitivity analysis. d. All of these statements are true.
All of these statements are true.
Which Excel® function allows you to count using more than one criterion? a. COUNTIF b. COUNTIFS c. HLOOKUP d. VLOOKUP
COUNTIFS
Gender and State are examples of which type of data?
Categorical data
Which of the following is not one of the "intermediate" features of Excel that the authors expect you to be able to use? a. SUMPRODUCT b. VLOOKUP c. IF d. NPV e. DIFFERENCEPRODUCT
DIFFERENCEPRODUCT
What is not one of the important themes of your Business Analytics: Data Analysis & Decision Making text? a. Data analysis b. Dealing with uncertainty c. Decision making d. Data mining
Data mining
1. Which statement is not true? a.Dealing with uncertainty includes measuring uncertainty. b. Dealing with uncertainty includes modeling uncertainty explicitly into the analysis. c. Dealing with uncertainty includes eliminating uncertainty by using the normal probability distribution. d. Dealing with uncertainty requires a basic understanding of probability.
Dealing with uncertainty includes eliminating uncertainty by using the normal probability distribution.
The four areas of a pivot table are a. Crosstabs, Fields, Rows, and Columns. b. Data, Count, Contingency, and Percentage. c. Filters, Rows, Columns, and Values. d. Sort, Rows, Columns, and Count.
Filters, Rows, Columns, and Values.
Which of the following best describes the concept of probability? a. It is a measure of the likelihood that a particular event will occur. b. It is a measure of the likelihood that a particular event will occur, given that another event has already occurred. c. It is a measure of the likelihood of the simultaneous occurrence of two or more events. d. None of these choices describe the concept of probability.
It is a measure of the likelihood that a particular event will occur.
Which of the following statements correctly describe estimation? a. It is the process of inferring the values of known population parameters from those of unknown sample statistics. b. It is the process of inferring the values of unknown sample statistics from those of known population parameters. c. It is the process of inferring the values of known sample statistics from those of unknown population parameters. d. It is the process of inferring the values of unknown population parameters from those of known sample statistics.
It is the process of inferring the values of unknown population parameters from those of known sample statistics.
If a value represents the 95th percentile, this means that 95% of all values in the data set are this value
Less than or equal to
Which of the following are the three most common measures of central location?
Mean, median and mode
The general form of a confidence interval is a. Point Estimate ± Multiple × Standard Error. b. Point Estimate ± Multiple + Standard Error. c. Point Estimate ± Multiple - Standard Error. d. Point Estimate ± Multiple ± Standard Error.
Point Estimate ± Multiple × Standard Error.
The number of degrees of freedom needed to construct 90% confidence interval for the difference between means when the data are gathered from paired samples, with 15 observations in each sample, is a. The difference between the means of appraised and sales house prices b. The difference between the proportion of defective items from two suppliers c. The difference in the mean life of two major brands of batteries d. The difference in the mean salaries for graduates in two different academic fields at a university
The difference between the means of appraised and sales house prices
Which statement is true for the following data values: 7,5,6,4,7,8, and 12?
The mean, median, and mode are all equal
1. Which statement is true of proportional sample sizes? a. The proportion of a stratum in the sample is independent of the proportion of that stratum in the population. b. The proportion of a stratum in the sample is the same as the proportion of that stratum in the population. c. The proportion of a stratum in the sample is greater than the proportion of that stratum in the population. d. The proportion of a stratum in the sample is less than the proportion of that stratum in the population.
The proportion of a stratum in the sample is the same as the proportion of that stratum in the population.
Which of the following statements is true? a. Probabilities must be negative. b. Probabilities must be greater than 1. c. The sum of all probabilities for a random variable must be equal to 1. d. The sum of all probabilities for a random variable must be equal to 0.
The sum of all probabilities for a random variable must be equal to 1.
1. Which of the following Excel® functions can be used for finding a particular value based on a comparison? a. IF b. SUMPRODUCT c. VLOOKUP d. NPV
VLOOKUP
1. Which equation shows the process of standardizing? a. E(X)=np b. Z=(X - u)/o c. f(x) = 1 - (o/u) d. E(Y) = u
Z=(X - u)/o
A 90% confidence interval can be used to reject the null hypothesis of a two-sided test at the 10% significance level if and only if a. a 90% confidence interval includes the hypothesized value of the parameter. b. a 90% confidence interval does not include the hypothesized value of the parameter. c. the null hypothesis is less than 0.05. d. the null hypotheses includes sampling error is greater than 0.05.
a 90% confidence interval does not include the hypothesized value of the parameter.
A 95% confidence interval can be used to reject the null hypothesis of a two-sided test at the 5% significance level if and only if a. a 95% confidence interval includes the hypothesized value of the parameter. b. a 95% confidence interval does not include the hypothesized value of the parameter. c. the null hypothesis is less than 0.05. d. the null hypotheses falls in the rejection region.
a 95% confidence interval does not include the hypothesized value of the parameter.
A useful way of comparing the distribution of a numerical variable across categories of some categorical variable is with a. a side-by-side box plot. b. a side-by-side pivot table. c. a side-by-side plot or side-by-side pivot table. d. neither a side-by-side box plot nor side-by-side pivot table.
a side-by-side plot or side-by-side pivot table.
Data analysis includes a. data description. b. data inference. c. the search for relationships in data. d. all of these choices.
all of these choices.
Examples of comparison problems include a. salary broken down by male and female subpopulations. b. cost of living broken down by region of a country. c. recovery rate for a disease broken down by patients who have taken a drug and patients who have taken a placebo. d. all of these choices.
all of these choices.
The decision making process includes a. optimization techniques for problems with no uncertainty. b. decision analysis for problems with uncertainty. c. sensitivity analysis. d. all of these choices.
all of these choices.
In statistical analysis, the burden of proof lies traditionally with the a. alternative hypothesis. b. null hypothesis. c. analyst. d. p-value.
alternative hypothesis.
If the number of observations in a single-variable data set is even the median. The mean is a measure of central tendency.
average of the two middle observations.
Categorizing age variables as "young," "middle-aged," and "elderly" is an example of: a. counting b. binning c. ordering d. categorizing e. value adding
binning
If P(A) = P(A|B), then events A and B are said to be a. can be any value between 0 and 1. b. can be any value between 0 and 0.70. c. cannot be larger than 0.30. d. can be any value between 0.30 and 0.70.
can be any value between 0 and 0.70.
The theorem that states that the sampling distribution of the sample mean is approximately normal when the sample size n is reasonably large is known as the _____ theorem. a. central limit b. central tendency c. simple random sample d. point estimate
central limit
We can infer that there is a strong relationship between two numeric variables when the points on a scatterplot a. cluster tightly around a straight line. b. are randomly scattered in no clear pattern. c. display a positive relationship. d. display a negative relationship.
cluster tightly around a straight line.
The normal distribution is a a. discrete distribution with two parameters. b. binomial distribution with only one parameter. c. density function of a discrete random variable. d. continuous distribution with two parameters.
continuous distribution with two parameters.
To examine relationships between two categorical variables, we can use a. counts and corresponding charts of the counts. b. scatter plots. c. histograms. d. boxplots. Tables used to display counts of a categorical variable a
counts and corresponding charts of the counts.
A sample of a population taken at one particular point in time is categorized as:
cross-sectional
The tables of counts that result from pivot tables are often called a. samples. b. sub-tables. c. populations. d. crosstabs.
crosstabs.
If you are constructing a confidence interval for a single mean, the length of the confidence interval will _____ with an increase in the sample size. a. decrease b. increase c. stay the same d. increase or decrease, depending on the sample data,
decrease
When the samples we want to compare pair in some natural way, such as a pretest/posttest for each person or husband/wife pairs, a more appropriate form of analysis is to not construct a confidence interval treating them as two separate variables, but instead to construct a confidence interval to estimate the mean a. difference. b. sum. c. ratio. d. total.
difference
The primary reason for standardizing random variables is to measure variables with a. different means and standard deviations on a non-standard scale. b. different means and standard deviations on a single scale. c. dissimilar means and standard deviations in like terms. d. similar means and standard deviations on two scales.
different means and standard deviations on a single scale.
Data that arise from counts are called:
discrete
There are two types of random variables, they are a. discrete and continuous. b. exhaustive and mutually exclusive. c. complementary and cumulative. d. real and unreal.
discrete and continuous.
Tables used to display counts of a categorical variable are called a. crosstabs. b. contingency tables. c. either crosstabs or contingency tables. d. neither crosstabs nor contingency tables.
either crosstabs or contingency tables.
What is the most common type of chart for showing the distribution of a numerical variable?
histogram
Where will you find "time" on a time series graph?
horizontal axis
If you increase the confidence level, the length of the confidence interval a. decreases. b. increases. c. stays the same. d. may increase or decrease, depending on the sample data.
increases
The length of the box in the box plot portrays
interquartile range
A discrete probability distribution a. is a set of possible values and a corresponding set of probabilities that sum to 1. b. is a modeling tool that can be used to incorporate uncertainty into models. c. can be estimated from long-run proportions. d. is the distribution of a single random variable.
is a set of possible values and a corresponding set of probabilities that sum to 1.
The p-value of a sample is the probability of seeing a sample with at _____ hypothesis as the sample actually observed. a. most as much evidence in favor of the null b. most as much evidence in favor of the alternative c. least as much evidence in favor of the null d. least as much evidence in favor of the alternative
least as much evidence in favor of the alternative
Correlation is useful only for a. assessing the weakness of a linear relationship. b. conveying the same information in a simpler format than a scatterplot. c. measuring the strength of a linear relationship. d. measuring the strength of a nonlinear relationship.
measuring the strength of a linear relationship.
In a box plot, the vertical line inside the box indicates the location of the
median
Let A and B be the events of the FDA approving and rejecting a new drug to treat hypertension, respectively. The events A and B are a. independent. b. conditional. c. unilateral. d. mutually exclusive.
mutually exclusive.
The t-distribution for developing a confidence interval for a mean has degrees of freedom equal to a. n + 2. b. n +1. c. n. d. n - 1.
n - 1
As the sample size increases, the t-distribution becomes more similar to the _____ distribution. 1. distribution. a. normal b. exponential c. binomial d. chi-square
normal
The chi-square goodness-of-fit test can be used to test for a. significance of sample statistics. b. difference between population means. c. normality. d. difference between population variances.
normality
A type II error occurs when the a. null hypothesis is incorrectly accepted when it is false. b. null hypothesis is incorrectly rejected when it is true. c. sample mean differs from the population mean. d. test procedure itself is fundamentally biased.
null hypothesis is incorrectly accepted when it is false.
A type I error occurs when the a. null hypothesis is incorrectly accepted when it is false. b. null hypothesis is incorrectly rejected when it is true. c. sample mean differs from the population mean. d. test procedure is fundamentally biased.
null hypothesis is incorrectly rejected when it is true.
A teacher who is trying to determine if the evidence supports the fact that a new method of teaching economics is more effective than a traditional one will conduct a _____ test. a. one-tailed b. two-tailed c. multi-tailed d. Paired
one-tailed
The tool that provides useful information about a data set by breaking it down into categories is a a. histogram. b. scatterplot. c. pivot table. d. spreadsheet.
pivot table.
The sampling mean is the ____ estimate for the population mean. a. random b. point c. simple d. Interval
point
A sample in which the sampling units are chosen from the population by means of a random mechanism is a _____ sample. a. probability b. judgmental c. convenience d. voluntary response
probability
A function that associates a numerical value with each possible outcome of an uncertain event is called a _____ variable. a. conditional b. random c. population d. sample
random
If the correlation of variables is close to 0, then we expect to see a(n) _____ on the scatterplot. a. upward sloping cluster of points b. downward sloping cluster of points c. cluster of points around a trendline d. random scatter of points with no apparent relationship
random scatter of points with no apparent relationship
As a measure of variability, what is defined as the maximum value minus the minimum value?
range
In order for the characteristics of a sample to be generalized to the entire population, it should be ________________ of the population.
representative
A two-tailed test is one where _____ lead to rejection of the null hypothesis. a. results in only one direction can b. negative sample means c. results in either of two directions can d. no results
results in either of two directions can
P(A) = 1 - P(A) is the a. addition rule. b. commutative rule. c. rule of complements. d. rule of opposites.
rule of complements.
Researchers may gain insight into the characteristics of a population by examining a
sample of the population
We study relationships among numerical variables using a. pie charts. b. counts. c. scatterplot charts. d. percentages.
scatterplot charts.
The value set for is known a is the a. rejection level. b. acceptance level. c. significance level. d. type II error in the hypothesis test.
significance level.
A sample chosen in such a way that every possible subset of same size has an equal chance of being selected is called a _____sample. a. cluster b. systematic random c. simple random d. stratified random
simple random
A histogram that is positively skewed is: skewed to the right
skewed to the right
The standard deviation of is usually called the a. standard error of the mean. b. standard error of the sample. c. standard error of the population. d. randomized standard error.
standard error of the mean.
The null hypothesis usually represents the a. theory the researcher would like to prove. b. preconceived ideas of the researcher. c. perceptions of the sample population. d. status quo of the situation being studied.
status quo of the situation being studied.
Selecting a random sample from each identifiable subgroup within a population is called _____ sampling. a. simple random b. systematic c. stratified d. Cluster
stratified
Correlation and covariance measure the a. strength of a linear relationship between two numerical variables. b. direction of a linear relationship between two numerical variables. c. strength and direction of a linear relationship between two numerical variables. d. strength and direction of a linear relationship between two categorical variables.
strength and direction of a linear relationship between two numerical variables.
If systematic sampling is chosen as the sampling technique, it is probably because a. systematic sampling has better statistical properties than simple random sampling. b. systematic sampling is more convenient. c. systematic sampling always results in more representative sampling than simple random sampling. d. systematic sampling gives every possible sample of the same size from the population an equal chance of being selected.
systematic sampling is more convenient.
When we replace with the sample standard deviation (s), we introduce a new source of variability and the sampling distribution becomes the a. t -distribution. b. F- distribution. c. chi-square distribution. d. normal distribution.
t -distribution
A restaurant manager claims that food servers at this restaurant make at least $15 per hour in tips. A random sample of 50 hours shows the mean amount of tips to be $12 per hour with standard deviation $0.75 per hour. What is the value of the test statistic that can be used to determine if there is convincing evidence that the mean amount of tips made per hour is less than the manager claimed? a. t = -7.165 b. t = -0.566 c. t = 9.172 d. t = -0.08
t = -0.566
Smaller p-values indicate more evidence in support of a. the null hypothesis. b. the alternative hypothesis. c. the quality of the researcher. d. none of these choices.
the alternative hypothesis.
1. In Excel®, the model outputs are a. the numeric values that result from combinations of inputs and decision variables through the use of logical formulas. b. useful for making formulas more readable. c. the variables a decision maker has control over to obtain the best solutions. d. useful for finding a particular value based on a comparison.
the numeric values that result from combinations of inputs and decision variables through the use of logical formulas.
In sampling, a population is a. the set of all humans. b. the set of all members about which a study intends to make inferences. c. the set of all members from whom data was collected. d. a random group of individuals, households, cities, or countries.
the set of all members about which a study intends to make inferences.
A variable is classified as ordinal if:
there is a natural ordering of categories
The daily closing values of the Dow Jones Industrial Average are examples of
time-series data
A line or curve superimposed on a scatterplot to quantify an apparent relationship is known as a(n) a. average. b. trend line. c. slope. d. function.
trend line.
The null and alternative hypotheses divide all possibilities into a. two sets that overlap. b. two non-overlapping sets. c. two sets that may or may not overlap. d. as many sets as necessary to cover all possibilities.
two non-overlapping sets.
The standard deviation of a probability distribution is a measure of a. variability of the distribution. b. central location. c. the shape of the distribution. d. skewness of the distribution.
variability of the distribution.
