stats
Which of the following is not a characteristic of a probability density function f(x)?
f(x) is symmetric around the mean.
One-way ANOVA assumes the population standard deviations are unknown and assumed unequal.
false
One-way ANOVA is used to determine if differences exist between the means of three or more populations under dependent sampling.
false
The between-treatments variance is the estimate of σ2 based on the variability due to chance.
false
Which of the following is considered an estimate?
line over X=12
The between-treatments variance is based on a weighted sum of squared differences between the
sample means and the overall mean of the data set
The probability that a normal random variable is less than its mean is
0.5
What are the two key properties of a discrete probability distribution?
0<_(X=x)<_1 and Ep(X=xi)1
the number of homes sold by a realtor during a month has the following probability distribution (CHART) what is the EXPECTED NUMBER of homes sold by the realtor during a month?
1.2
How many parameters are needed to fully describe any normal distribution?
2
The following is an incomplete ANOVA table. CHART The mean square error is _
9.375
Which of the following is considered an estimator?
A line over a capital X
Which of the following represents a subjective probability?
A skier believes she has a 10% chance of winning a gold medal.
What is a simple event?
An event that contains only one outcome of a sample space
In what way(s) is(are) the concept of geometric mean useful?
Both in evaluating investment returns and in calculating average growth rates
The following table shows the distribution of employees in an organization. Martha Foreman, an analyst, wants to see if race has a bearing on the position a person holds with this company. CHART Which of the following is a way to ensure all expected frequencies in each cell of the above table are five or more?
Combine the expected frequencies for seniorities Manager and Director.
Which of the following is a data preparation task?
Counting relevant variables
When visualizing a numerical variable, what is an ogive used to plot?
Cumulative frequency or cumulative relative frequency of each class against the upper limit of the corresponding class
A 99% confidence interval for the population mean yields the following results: [−3.79, 5.86]. At the 1% significance level, what decision should be made regarding the following hypothesis test with H0:μ = 0,HA:μ ≠ 0?
Do not reject H0; we cannot conclude that the mean differs from zero.
What is the name of the variable that is used to predict another variable?
Explanatory
Which of the following statements about regression analysis is FALSE?
It can establish cause-and-effect relationships.
Suppose you want to perform a test to compare the mean GPA of all freshmen with the mean GPA of all sophomores in a college? What type of sampling is required for this test?
Independent sampling with numerical data
Which of the following is not a form of bias?
Information from the sample is typical of information in the population.
Which of the following best describes a frequency distribution for a categorical variable?
It groups data into categories and records the number of observations in each category.
What is(are) characteristic(s) of the geometric mean?
It is always less than or equal to the arithmetic mean.
How does the variance of the sample mean compare to the variance of the population?
It is smaller and therefore suggests that averages have less variation than individual observations.
Which of the following is not a restriction for comparing two population means?
Matched-pairs sampling
Which of the following scales represents the least sophisticated level of measurement?
Nominal
If A and B are independent events, which of the following is correct?
P(A/B)=P(A)
If A and B are independent events, which of the following is correct?
P(AB)=P(A)P(AB)=P(A)
Let A and B be two independent events with P(A) = 0.40 and P(B) = 0.20. Which of the following is correct?
P(A∪B)=0.52P(A∪B)=0.52
For which of the following data sets will a pie chart be most useful?
Percentage of net sales by product for Lenovo in Year 1
The accompanying chart shows the number of books written by each author in a collection of cookbooks. What type of data is being represented? (CHART)
Qualitative, nominal
When using the empirical rule, which of the following assumptions is made?
The data are approximately symmetric and bell-shaped.
When using a polygon to visualize a numerical variable, what does each point represent?
The midpoint of a particular class and its associated frequency or relative frequency
Which of the following variables is not continuous?
The number of obtained heads when a fair coin is tossed 20 times
Which of the following is an example of a uniformly distributed random variable?
The scheduled arrival time of a cable technician.
Which of the following statements regarding the sampling distribution of the sample mean is TRUE?
The variance of the sample mean is smaller than the variance of all individual observations in the population.
Let X be normally distributed with mean μ and standard deviation σ > 0. Which of the following is false about the z value corresponding to a given xvalue?
The z value corresponding to a given value of x assumes any value between 0 and 1.
The data represents the stock price for Google at the end of the past four quarters. Which of the following types of data best describe these values?
Time series
Which of the following is an example in which a one-way ANOVA test is appropriate?
To determine if mean test scores differ between the four sections.
When calculating the standard error of (line over X1 - line over X2), under what assumption do you pool the sample variances s22s22 and S 2/2 and S 2/2 ?
Unknown population variances that are assumed equal.
What is(are) the most widely used measure(s) of dispersion?
Variance and standard deviation
Which of the following statements about variance is the most accurate?
Variance is the average of the squared deviations from the mean.
The coefficient of variation is best described as
a relative measure of dispersion
A sample space contains
all possible outcomes of an experiment.
The alternative hypothesis typically
contests the status quo, for which a corrective action may be required
A(n) __________ variable is characterized by infinitely uncountable values and can take any value within interval.
continuous
A Type II error occurs when we
do not reject the null hypothesis when it is actually false
Mutually exclusive events
do not share common outcomes
Excel and virtually all other statistical packages report the p-value
for a two-tailed test that assesses whether the regression coefficient differs from zero
Unlike the coefficient of determination, the sample correlation coefficient in a simple linear regression
indicates whether the slope of the regression line is positive or negative
In general, the null and alternative hypotheses are ___
mutually exclusive
When we reject the null hypothesis when it is actually false, we have committed
no error
When reading published statistics (numerical facts), you should
only believe those statistics that are adequately supported.
The R2 of a multiple regression of y on x1 and x2 measures the
percentage of the variation in y that is explained by the sample regression equation
The one-way ANOVA null hypothesis is rejected when the
ratio of the within-treatments variance and the between-treatments variance is significantly greater than 1
Simple linear regression analysis differs from multiple regression analysis in that
simple linear regression uses only one explanatory variable
For the chi-square test of a contingency table, the expected cell frequencies are found as eij=(Rowitotal)(Columnjtotal)Samplesizeeij=(Row i total)(Column j total)Sample size which is the same as
the cell probability multiplied by the sample size
we can think of the expected value of a random variable x as
the long-run average of the random variable values generated over infinitely many independent repetitions
We can think of the expected value of a random variable X as
the long-run average of the random variable values generated over infinitely many independent repetitions.
If the null hypothesis is rejected at a 1% significance level, then
the null hypothesis will be rejected at a 5% significance level
When testing the difference between two population means under independent sampling, we use the z distribution if
the population variances are known
Consider the following sample regression equation yˆy^ = 150 − 20x, where y is the demand for Product A (in 1,000s) and xis the price of the product (in $). The slope coefficient indicates that if
the price of Product A increases by $1, then we predict the demand to decrease by 20,000
The standard error of the estimate measures _
the standard deviation of the random error
The study of statistics is NOT about
the study of mind and consciousness.
Events are collectively exhaustive if
they contain all outcomes of an experiment
We use ANOVA to test for differences between population means by examining the amount of variability between the samples relative to the amount of variability within the samples.
true
The chi-square test of a contingency table is a test of independence for
two qualitative variables
The coefficient of determination R2 is __
usually higher than adjusted R2
The empirical rule can be used to estimate some proportions
when it is approximately symmetric and bell-shaped.
A new sales training program has been instituted at a rent-to-own company. Prior to the training, 10 employees were tested on their knowledge of products offered by the company. Once the training was completed, the employees were tested again in an effort to determine whether the training program was effective. Scores are known to be normally distributed. The sample scores on the tests are listed next. Use pretest score as µ1 for population 1 and posttest score as µ2 for population 2, or µD as the mean of the difference calculated as pretest score minus posttest score. Which of the following are the appropriate hypotheses to determine if the training increases scores?
H0: µD ≥ 0, HA: µD < 0
Which of the following set of hypotheses is used to test if the mean of the first population is smaller than the mean of the second population, using matched-paired sampling?
H0: µD ≥ 0,HA: µD < 0
A police chief wants to determine if crime rates are different for four different areas of the city (East(1), West(2), North(3), and South(4) sides), and obtains data on the number of crimes per day in each area. The one-way ANOVA table is shown below. CHART The competing hypotheses about the mean crime rates are _
H0: μ1 = μ2 = μ3 = μ4, HA: Not all population means are equal
A researcher with the Ministry of Transportation is commissioned to study the drive times to work (one-way) for U.S. cities. The underlying hypothesis is that average commute times are different across cities. To test the hypothesis, the researcher randomly selects six people from each of the four cities and records their one-way commute times to work. Refer to the below data on one-way commute times (in minutes) to work. Note that the grand mean is 36.625. CHART The competing hypotheses about the mean commute times are
H0: μ1 = μ2 = μ3 = μ4, HA: Not all population means are equal
Tiffany & Company has been the world's premier jeweler since 1837. The performance of Tiffany's stock is likely to be strongly influenced by the economy. Monthly data for Tiffany's risk-adjusted return and the risk-adjusted market return are collected for a five-year period (n = 60). The accompanying table shows the regression results when estimating the Capital Asset Pricing Model (CAPM) model for Tiffany's return. CHART You would like to determine whether an investment in Tiffany's is riskier than the market. When conducting this test, you set up the following competing hypotheses:
H0:β ≤ 1; HA:β > 1
Consider the following simple linear regression model: y = β0 + β1x + ε. When determining whether xsignificantly influences y, the null hypothesis takes the form
H0:β1 = 0
A sociologist wishes to study the relationship between happiness and age. He interviews 24 individuals and collects data on age and happiness, measured on a scale from 0 to 100. He estimates the following model: Happiness = β0+ β1Age + ε. The following table summarizes a portion of the regression results. CHART When defining whether age is significant in explaining happiness, the competing hypotheses are _
H0:β1 = 0; HA:β1 ≠ 0
A marketing analyst wants to examine the relationship between sales (in $1,000s) and advertising (in $100s) for firms in the food and beverage industry and so collects monthly data for 25 firms. He estimates the model:Sales = β0 + β1 Advertising + ε. The following table shows a portion of the regression results. CHART Which of the following are the competing hypotheses used to test whether Advertising is significant in predicting Sales?
H0:β1 = 0; HA:β1 ≠ 0.
Consider the following simple linear regression model: y = β0 + β1x + ε. When determining whether there is a one-to-one relationship between x and y, the null hypothesis takes the form
H0:β1 = 1
A sports analyst wants to exam the factors that may influence a tennis player's chances of winning. Over four tournaments, he collects data on 30 tennis players and estimates the following model: Win = β0 + β1 Double Faults + β2 Aces + ε, where Win is the proportion of winning, Double Faults is the percentage of double faults made, and Aces is the number of aces. A portion of the regression results are shown in the accompanying table. CHART When testing whether the explanatory variables jointly influence the response variable, the null hypothesis is __
H0:β1 = β2 = 0
A real estate analyst believes that the three main factors that influence an apartment's rent in a college town are the number of bedrooms, the number of bathrooms, and the apartment's square footage. For 40 apartments, she collects data on the rent (y, in $), the number of bedrooms (x1), the number of bathrooms (x2), and its square footage (x3). She estimates the following model: Rent = β0 + β1 Bedroom + β2 Bath + β3Sqft + ε. The following table shows a portion of the regression results. CHART When testing whether the explanatory variables jointly influence the response variable, the null hypothesis is
H0:β1 = β2 = β3 = 0
Consider the following simple linear regression model: y = β0 + β1x + ε. When determining whether there is a negative linear relationship between x and y, the alternative hypothesis takes the form
HA:β1 < 0
Consider the following simple linear regression model: y = β0 + β1x + ε. When determining whether there is a positive linear relationship between x and y, the alternative hypothesis takes the form _
HA:β1 > 0
What graphical tool is best used to display the relative frequency of a numerical variable?
Histogram
For a given sample size and population standard deviation, which of the following is true in the interval estimation of the population mean?
If the confidence level is greater, the interval is wider.
For a given confidence level and sample size, which of the following is true in the interval estimation of the population mean when σ is known?
If the population standard deviation is greater, the interval is wider.
For a given confidence level and population standard deviation, which of the following is true in the interval estimation of the population mean?
If the sample size is bigger, the interval is narrower.
John would like to conduct a survey in his neighborhood to get homeowners' opinion on the Delmarva proposal to switch to natural gas. Which of the following is an example of a stratified sample
John divides the population into two-story, split-level, and ranch houses. Then, he selects a proportional number of houses from each group.
Peggy would like to conduct a survey in her neighborhood to get homeowners' opinions on the Delmarva proposal to switch to natural gas. Which of the following is an example of a convenience sample?
John selects the first 25 homes that he passes as he walks into the entrance of the development.
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?
Mean, median, and mode
Which five values are graphed on a box plot?
Min, Quartile 1, Median, Quartile 3, Max
The accompanying table shows the regression results when estimating y = β0 + β1x + ε. CHART Is x significantly related to y at the 5% significance level?
No, because the p-value of 0.0745 is greater than 0.05.
Frequency distributions may be used to describe which of the following types of data?
Nominal, ordinal, interval, and ratio data
Which of the following is the necessary condition for creating confidence intervals for the population mean?
Normality of the estimator
Which of the following sets of outcomes described below in I and II represent mutually exclusive events? "Your final course grade is an A"; "Your final course grade is a B." "Your final course grade is an A"; "Your final course grade is a Pass."
Only I represents mutually exclusive events.
An undergraduate student's status (freshman, sophomore, junior, or senior) is an example of which scale of measurement?
Ordinal scale
It is known that the length of a certain product X is normally distributed with μ = 20 inches. How is the probability P(X < 20) related to P(X < 16)?
P(X < 20) is greater than P(X < 16).
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 greater than P(X < 16).
What is the most typical form of a calculated confidence interval?
Point estimate ± Margin of error
Which of the following is an example of time series data?
Quarterly housing stats collected over the last 60 years
Which of the following scales represents the strongest level of measurement?
Ratio
What is the decision rule when using the p-value approach to hypothesis testing?
Reject H0 if the p-value < α.
When conducting a hypothesis test, which of the following decisions represents an error?
Rejecting the null hypothesis when it is true.
Which of the following represents a population and a sample from that population?
Residents of Albany, New York, and registered voters in Albany, New York
Which of the following is an example of cross-sectional data?
Results of market research testing consumer preferences for sodaCorrect
When the required sample size calculated by using a formula is not a whole number, what is the best choice for the required sample size?
Round the result of the calculation up to the nearest whole number.
You have a point-of-sale data set that provides information on time of sale, products bought, and payment methods customers used to complete their purchases. You want to compare purchases made by cash versus those made by credit card. How should the data be best prepared to make comparisons between the two types of purchases?
Subset the data by method of payment
he cumulative distribution function F(x) of a continuous random variable X with the probability density function f(x) is which of the following?
The area under f over all values that are x or less.
A machine that is programmed to package 1.20 pounds of cereal is being tested for its accuracy in a sample of 36 cereal boxes: the sample mean filling weight is calculated as 1.22 pounds. The population standard deviation is known to be 0.06 pounds. Which of the following conclusions is correct with a 95% confidence level?
The machine is operating properly because the interval contains the target.
The national average for an eighth-grade reading comprehension test is 73. A school district claims that its eighth-graders outperform the national average. In testing the school district's claim, how does one define the population parameter of interest?
The mean score on the eighth-grade reading comprehension test
Which of the following does not represent a continuous random variable?
The number of customer arrivals to a bank between 10 am and 11 am.
When some objects are randomly selected, which of the following is true?
The order in which objects are selected does not matter in combinations.
For both categorical and numerical variables, what is the difference between the relative frequency and the percent frequency?
The percent frequency equals the relative frequency multiplied by 100.
Which of the following is the assumption that is not applicable for a one-way ANOVA test?
The population standard deviations are not all equal.
Which of the following is FALSE about a continuous random variable?
The probability that its value is within a specific interval is equal to one.
What is the relationship between the variance and the standard deviation?
The standard deviation is the positive square root of the variance.
A survey is designed to collect data on students' evaluations of their instructor's teaching performance. Which of the following situations most likely results in social-desirability biases?
The survey is administered in class with the instructor in the room the entire time.
What does it mean when we say that the tails of the normal curve are asymptotic to the x axis?
The tails get closer and closer to the x axis but never touch it.
How do the tdf and z distributions differ?
The tdf distribution has broader tails (it is flatter around zero).
Which of the following statements is TRUE about tests of significance to determine whether there is evidence of a linear relationship between the response variable and the explanatory variables?
The test of individual significance is the same as the test of joint significance for a simple linear regression model.
What conditions are required by the central limit theorem before a confidence interval of the population mean may be created?
The underlying population need not be normally distributed if the sample size is 30 or more.
Which of the following capabilities does Analysis of Relative Location provide?
They make statements regarding the percentage of data values that fall within some number of standard deviations from the mean.
Which type of data, cross-sectional versus time series, is more important to research?
Time series data and cross-sectional data are equally as valuable in different types of research.
Which of the following is an example of a chi-square test for independence?
To determine whether the likelihood of college admission depends on the race of the applicants.
What is the purpose of calculating a confidence interval?
To provide a range of values that, with a certain measure of confidence, contains the population parameter of interest.
Confidence intervals of the population mean may be created for the cases when the population standard deviation is known or unknown. How are these two cases treated differently?
Use the z table when σ is known; use the t table when σ is unknown.
Is it possible for a data set to have more than one mode?
Yes, if two or more values in a data set occur with the most frequency and the frequency is greater than one.
a consumer who is risk neutral is best charaterized as
a consumer who completely ignores risk and makes his or her decisions based solely on expected values
A consumer who is risk averse is best characterized as
a consumer who demands a positive expected gain as compensation for taking risk
a consumer who is risk averse is best characterized as
a consumer who demands a positive expected gain as compensation for taking risk
how would you characterize a consumer who is risk loving?
a consumer who may accept a risky prospect if the expected gain is negative.
Consider the following hypotheses that relate to the medical field: H0: A person is free of disease. HA: A person has disease. In this instance, a Type I error is often referred to as
a false positive
which of the following represents a subjective probability?
a skier believes she has a 10% chance of winning a gold medal
A sample space contains _
all possible outcomes of an experiment.
Chebyshev's theorem is applicable when the data are
any shape
The tdf distribution is similar to the z distribution because
as the degrees of freedom go to infinity, the t distribution converges to the z distribution and both have asymptotic tails—that is, their tails become closer and closer to the horizontal axis but never touch it
The chi-square test of a contingency table is valid when the expected cell frequencies are
at least 5
The variability due to chance, also known as the within-treatments variance, is the estimate of σ2 which is not based on the variability
between the sample means
Population parameters are difficult to calculate due to
both cost prohibitions on data collection and the infeasibility of collecting data on the entire population.
When constructing a frequency distribution for a numerical variable, it is important to remember that
classes are mutually exclusive
A probability based on logical analysis rather than on observation or personal judgment is best referred to as a(n)
classical probability
Consider the following sample regression equation yˆy^ = 150 − 20x, where y is the demand for Product A (in 1,000s) and x is the price of the product (in $). If the price of the good increases by $3, then we expect demand for Product A to
decrease by 60,000
For a given sample size n,
decreasing the probability of a Type I error α will increase the probability of a Type II error β
The two branches of the study of statistics are generally referred to as
descriptive and inferential statistics.
Statistics are used to estimate population parameters, particularly when it is impossible or too expensive to poll an entire population. A particular value of a statistic is referred to as a
estimate
In order to summarize a categorical variable, a useful tool is a
frequency distribution
The Fahrenheit scale for measuring temperature would be classified as a(n)
interval scale.
The central limit theorem states that, for any distribution, as n gets larger, the sampling distribution of the sample mean
is closer to a normal distribution
A continuous random variable has the uniform distribution on the interval [a, b] if its probability density function f(x) ______.
is constant for all x between a and b, and 0 otherwise
The advantage of using mean absolute deviation rather than variance as a measure of dispersion is that mean absolute deviation
is less sensitive to extreme deviations
which of the following statements is the most accurate about a binomial random variable?
it counts the number of successes in a given number of trials.
which of the following statements is the most accurate about a poisson random variable?
it counts the number of successes in a specific time or space interval
When two regression models applied on the same data set have the same response variable but a different number of explanatory variables, the model that would evidently provide the better fit is the one with a
lower standard error of the estimate and a higher adjusted coefficient of determination
When comparing two population means, their hypothesized difference
may assume any value
If the underlying populations cannot be assumed to be normal, then by the central limit theorem, the sampling distribution of (line over X1-line over X2) is approximately normal only if both sample sizes are sufficiently large—that is, when
n1 ≥ 30 and n2 ≥ 30
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." This data is best classified as
nominal scale.
Tiffany & Company has been the world's premier jeweler since 1837. The performance of Tiffany's stock is likely to be strongly influenced by the economy. Monthly data for Tiffany's risk-adjusted return and the risk-adjusted market return are collected for a five-year period (n = 60). The accompanying table shows the regression results when estimating the Capital Asset Pricing Model (CAPM) model for Tiffany's return. CHART When testing whether there are abnormal returns, the conclusion to the test is at the 5% significance level is to
not reject H0, we cannot conclude there are abnormal returns
If the p-value for a hypothesis test is 0.07 and the chosen level of significance is α = 0.05, then the correct conclusion is to
not reject the null hypothesis
A sample of 200 monthly observations is used to run a simple linear regression: Returns = β0 + β1 Leverage + ε. A 5% level of significance is used to study if leverage has a significant influence on returns. The value of the test statistic for the regression coefficient of Leverage is calculated as t198 = −1.09, with an associated p-value of 0.2770. The correct decision is to
not reject the null hypothesis; we cannot conclude that leverage significantly explains returns
A sample statistic is an estimate of
population parameter.
Selection bias occurs when
portions of the population are excluded from the consideration for the sample
When conducting a hypothesis test for a given sample size, if the probability of a Type I error decreases, then the _
probability of incorrectly not rejecting the null hypothesis increases
An analyst collects data on the weekly closing price of gold throughout a year. The scale of this data is
ratio scale.
The accompanying table shows the regression results when estimating y = β0 + β1x1 + β2x2 + β3x3 + ε. CHART When testing whether the explanatory variables are jointly significant at the 5% significance level, the conclusion is to
reject H0, and conclude that the explanatory variables are jointly significant
A marketing analyst wants to examine the relationship between sales (in $1,000s) and advertising (in $100s) for firms in the food and beverage industry and so collects monthly data for 25 firms. He estimates the model:Sales = β0 + β1 Advertising + ε. The following table shows a portion of the regression results. CHART When testing whether Advertising is significant at the 10% significance level, the conclusion is to
reject H0; we can conclude advertising is significant
Tiffany & Company has been the world's premier jeweler since 1837. The performance of Tiffany's stock is likely to be strongly influenced by the economy. Monthly data for Tiffany's risk-adjusted return and the risk-adjusted market return are collected for a five-year period (n = 60). The accompanying table shows the regression results when estimating the Capital Asset Pricing Model (CAPM) model for Tiffany's return. CHART When testing whether the beta coefficient is significantly greater than one, the relevant critical value at the 5% significance level is t0.05,58 = 1.672. The conclusion to the test is to
reject H0; we can conclude that the return on Tiffany stock is riskier than the return on the market
If the p-value for a hypothesis test is 0.027 and the chosen level of significance is α = 0.05, then the correct conclusion is to __________
reject the null hypothesis
To test if the mean IQ of employees in an organization is greater than 100, a sample of 30 employees is taken and the value of the test statistic is computed as t29 = 2.42 If we choose a 5% significance level, we
reject the null hypothesis and conclude that the mean IQ is greater than 100
A Type I error occurs when we
reject the null hypothesis when it is actually true
A local courier service advertises that its average delivery time is less than 6 hours for local deliveries. When testing the two hypotheses, H0: μ ≥ 6 and HA: μ < 6, μ stand fo
the mean delivery time
The owner of a large car dealership believes that the financial crisis decreased the number of customers visiting her dealership. The dealership has historically had 800 customers per day. The owner takes a sample of 100 days and finds the average number of customers visiting the dealership per day was 750. Assume that the population standard deviation is 350. The population parameter to be tested is _
the mean number of customers visiting the dealership per day
A researcher with the Ministry of Transportation is commissioned to study the drive times to work (one-way) for U.S. cities. The underlying hypothesis is that average commute times are different across cities. To test the hypothesis, the researcher randomly selects six people from each of the four cities and records their one-way commute times to work. Refer to the below data on one-way commute times (in minutes) to work. Note that the grand mean is 36.625. CHART Based on the sample standard deviation, the one-way ANOVA assumption that is likely not met is
the population standard deviations are assumed to be equal.
Consider the following sample regression equation yˆy^ = 200 + 10x, where y is the supply for Product A (in 1,000s) and xis the price of Product A (in $). The slope coefficient indicates that if
the price of Product A increases by $1, then we predict the supply to increase by 10,000
Two or more random samples are considered independent if
the process that generates one sample is completely separate from the process that generates the other sample
The ages of MBA students at a university are normally distributed with a known population variance of 10.24. Suppose you are asked to construct a 95% confidence interval for the population mean age if the mean of a sample of 36 students is 26.5 years. If a 99% confidence interval is constructed instead of a 95% confidence interval for the population mean, then _
the resulting margin of error will increase and the risk of reporting an incorrect interval will decrease
For the chi-square test of a contingency table, the expected cell frequencies are found as
the row total multiplied by the column total divided by the sample size
According to the central limit theorem, the distribution of the sample means is normal if
the sample size n ≥ 30
A hypothesis test regarding the population mean is based on
the sampling distribution of the sample mean
The choice of an appropriate test for comparing two population means depends on whether we deal with the following except:
the sum or product of a single parameter
Bias can occur in sampling. Bias refers to
the tendency of a sample statistic to systematically over- or underestimate a population parameter
The standard error of the estimate measures
the variability of the observed y-values around the predicted y-values
If the chosen significance level is α = 0.05, then
there is a 5% probability of rejecting a true null hypothesis
Nonresponse bias occurs when
those responding to a survey or poll differ systematically from the nonrespondents
A 90% confidence interval is constructed for the population mean. If a 95% confidence interval had been constructed instead (everything else remaining the same), the width of the interval would have been ________ and the probability of making an error would have been
wider, smaller
Consider the following simple linear regression model: y = β0 + β1x + ε. The explanatory variable is
x
The accompanying table shows the regression results when estimating y = β0 + β1x1 + β2x2 + β3x3 + ε. CHART At the 5% significance level, which of the following explanatory variable(s) is(are) individually significant?
x1 and x2
Consider the following simple linear regression model: y = β0 + β1 + ε. The response variable is
y
A city in California spent $6 million repairing damage to its public buildings in Year 1. The following table shows the categories where the money was directed. (CHART) How much did the city spend to fix damage caused by mold?
$720,000
In a simple linear regression model, if the points on a scatter diagram lie on a straight line with a negative slope, which of the following is the coefficient of determination?
+0
A sample regression equation is given by yˆy^ = −100 + 0.5x. If x = 20, the predicted value of y is
-90
what is the probability that x is greater than 3?
.25
Consider the following frequency distribution. (CHART) What proportion of the observations are at least 15 but less than 18?
.30
Two hundred people were asked if they had read a book in the last month. The accompanying contingency table, cross-classified by age, is produced. (CHART) The probability that a respondent read a book in the last month and is at least 30 years old is the closest to
.33
Let P(A)=0.3andP(B)=0.4.P(A)=0.3 and P(B)=0.4. Suppose A and B are independent. What is the value of P(B|A)?
.4
The 150 residents of the town of Wonderland were asked their age and whether they preferred vanilla, chocolate, or swirled frozen yogurt. The results are displayed next. (CHART) What is the probability that a randomly selected customer prefers vanilla?
.40
what is the probability that x equals 2?
.44
Two hundred people were asked if they had read a book in the last month. The accompanying contingency table, cross-classified by age, is produced. (CHART) The probability that a respondent is at least 30 years old is the closest to
.50
on a particular production line, the likelihood that a light bulb is defective is 5%
.50 and .475
In a simple linear regression model, if the plots on a scatter diagram lie on a straight line, which of the following is the standard error of the estimate?
0
The time to complete the construction of a soapbox derby car is normally distributed with a mean of three hours and a standard deviation of one hour. Find the probability that it would take exactly 3.7 hours to construct a soapbox derby car.
0.0000
Peter applied to an accounting firm and a consulting firm. He knows that 30% of similarly qualified applicants receive job offers from the accounting firm, while only 20% of similarly qualified applicants receive job offers from the consulting firm. Assume that receiving an offer from one firm is independent of receiving an offer from the other. What is the probability that both firms offer Peter a job?
0.06
In the following table, individuals are cross-classified by their age group and income level. CHART Low 120, 150, 160 Med 100, 160, 180 High 75, 100, 160 Which of the following is the estimated joint probability for the "low income and 21-35 age group" cell?
0.0996
The contingency table below provides frequencies for the preferred type of exercise for people under the age of 35, and those 35 years of age or older. Find the probability that an individual prefers biking given that he or she is 35 years old or older.
0.1698
The contingency table below provides frequencies for the preferred type of exercise for people under the age of 35, and those 35 years of age or older. Find the probability that an individual prefers biking given that he or she is 35 years old or older. Age GroupPreferred Form of Exercise (RunningBikingSwimming) Under 35 years 157, 121, 79, total 357 35 years or older 45, 27, 87, total 159 Total 202, 148, 166, 516
0.1698
Consider the following cumulative function for the discrete random variable x x 1 2 3 4 5 p(x<_x) 0.10 0.35 0.75 0.85 1.00
0.25
Two hundred people were asked if they had read a book in the last month. The accompanying contingency table, cross-classified by age, is produced. Under 30 30+ Yes 76, 65 No 24, 35 The probability that a respondent read a book in the last month and is at least 30 years old is the closest to _______
0.33
Alex is in a hurry to get to work and is rushing to catch the bus. She knows that the bus arrives every six minutes during rush hour, but does not know the exact times the bus is due. She realizes that from the time she arrives at the stop, the amount of time that she will have to wait follows a uniform distribution with a lower bound of 0 minutes and an upper bound of six minutes. What is the probability that she will have to wait less than two minutes?
0.3333
The contingency table below provides frequencies for the preferred type of exercise for people under the age of 35 and those 35 years of age or older. Find the probability that an individual prefers running. (CHAT)
0.3915
The contingency table below provides frequencies for the preferred type of exercise for people under the age of 35 and those 35 years of age or older. Find the probability that an individual prefers running. Age GroupPreferred Form of Exercise (Running Biking Swimming) Under 35 years 157, 121, 79, total 357. 35 years or older 45, 27, 87, total 159. Total 202, 148, 166, total 516.
0.3915
Let P(A)=0.3 and P(B)=0.4.P(A)=0.3 and P(B)=0.4. Suppose A and B are independent. What is the value of P(B|A)?
0.4
The 150 residents of the town of Wonderland were asked their age and whether they preferred vanilla, chocolate, or swirled frozen yogurt. The results are displayed next. (Chocolate, Vanilla, Swirl) Under 25 years old 40, 20, 15 At least 25 years old 15, 40, 20 What is the probability that a randomly selected customer prefers vanilla?
0.40
Two hundred people were asked if they had read a book in the last month. The accompanying contingency table, cross-classified by age, is produced. Under 30, 30+ Yes 76, 65 No 24, 35 The probability that a respondent is at least 30 years old is the closest to ______.
0.50
on a particular production line, the likelihood that a light bulb is defective is 5%. ten light bulbs are randomly selected. what are the mean and variance of the number of defective bulbs?
0.50 and 0.475
What is the standard deviation of the number of cars sold by the salesperson during a week?
0.75
What is the standard deviation of the number of homes sold by the realtor during a month?
0.75
the number of homes sold by a realtor during a month has the following probability distribution (CHART) what is the STANDARD DEVIATION of the number of homes sold by the realtor during a month?
0.75
what is the STANDARD DEVIATION of the number of cars sold by the salesperson during a week?
0.75
for a particular clothing store, a marketing firm finds that 16% of 10% off coupons delivered by mail are redeemed. suppose six costumers are randomly selected and are mailed $10 off coupons. What is the expected number. of coupons that will be redeemed?
0.96%
what are the two key properties of a discrete probability distribution?
0<_P(X=x)<_1 and EP(X=xi)=1
In the following table, likely voters' preferences of two candidates are cross-classified by gender. CHART male 150, 100 female 100, 120 For the chi-square test of independence, the assumed degrees of freedom are
1
The following is an incomplete ANOVA table. CHART The value of the test statistic is
1.333
according to geologists, the San Francisco Bay Area experiences five earthquakes with a magnitude of 6.5 or greater every 100 years. what is the standard deviation of the number of earthquakes with a magnitude of 6.5 or greater striking the San Francisco Bay Area in the next 40 years?
1.414
according to a department of labor report, the city of Detroit had a 20% unemployment rate in May. Eight working-age residents were chosen at random. What was the expected number of unemployed residents, when eight working-age residents were randomly selected?
1.6
What is zαl2 for a 90% confidence interval of the population mean?
1.645
Consider the following probability distribution Xi P(X=x i) 0 0.1 1 0.2 2 0.4 3 0.3 the expected value is?
1.90
consider the following probability distribution (CHART) the expected value is
1.90
What is zα/2 for a 95% confidence interval of the population mean?
1.96
The ages of MBA students at a university are normally distributed with a known population variance of 10.24. Suppose you are asked to construct a 95% confidence interval for the population mean age if the mean of a sample of 36 students is 26.5 years. What is the margin of error for a 95% confidence interval for the population mean?
1.96(3.20/6)
The height of the probability density function f(x) of the uniform distribution defined on the interval [a, b] is ______.
1/(b − a) between a and b, and zero otherwise
If there are five treatments under study, the number of pairwise comparisons is
10
In the following table, individuals are cross-classified by their age group and income level. CHART Assuming age group and income are independent, the expected "low income and 21-35 age group" cell frequency is
105.27
Consider the following frequency distribution. (CHART) How many observations are less than 21?
12
What is the expected number of homes sold by the realtor during a month?
12
The following table shows the distribution of employees in an organization. Martha Foreman, an analyst, wants to see if race has a bearing on the position a person holds with this company. CHART The column total for directors is
16
according to geologists, the San Francisco Bay Area experiences five earthquakes with a magnitude of 6.5 or greater every 100 years. what is the expected value of the number of earthquakes with a magnitude of 6.5 or greater striking the San Francisco Bay Area in the next 40 years?
2.0000
An analyst constructed the following frequency distribution on the monthly returns for 50 selected stocks (CHART) The number of stocks with returns of 0% up to 10% is
25
The following is an incomplete ANOVA table. CHART The sum of squares due to treatments is
25
A daily mail is delivered to your house between 1:00 p.m. and 5:00 p.m. Assume delivery times follow the continuous uniform distribution. Determine the percentage of mail deliveries that are made after 4:00 p.m.
25%
Consider the following sample regression equation yˆy^ = 200 + 10x, where y is the supply for Product A (in 1,000s) and xis the price of Product A (in $). If the price of Product A is $5, then we expect supply to be
250,000
Suppose Bank of America would like to investigate if the credit score and income level of an individual are independent of one another. Bank of America selected a random sample of 400 adults and asked them to report their credit score range and their income range. The following contingency table presents these results. CHART The expected number of individuals with income less than $50,000 and a credit score between 650 and 750 is
26.0
Over the entire six years that students attend an Ohio elementary school, they are absent, on average, 28 days due to influenza. Assume that the standard deviation over this time period is σ = 9 days. Upon graduation from elementary school, a random sample of 36 students is taken and asked how many days of school they missed due to influenza. What is the expected value for the sampling distribution of the average number of school days missed due to influenza?
28
A police chief wants to determine if crime rates are different for four different areas of the city (East(1), West(2), North(3), and South sides), and obtains data on the number of crimes per day in each area. The one-way ANOVA table is shown below. CHART The degrees of freedom for the hypothesis test are
3, 20
Consider the partially completed one-way ANOVA summary table. CHART The value of the test statistic is
3.0
The following table shows the distribution of employees in an organization. Martha Foreman, an analyst, wants to see if race has a bearing on the position a person holds with this company. CHART The row total for Asians is
31
An analyst constructed the following frequency distribution on the monthly returns for 50 selected stocks. (CHART) The number of stocks with returns of less than 10% is
33
The following is a list of five of the world's busiest airports by passenger traffic for Year 1. (CHART) The percentage of passenger traffic in the five busiest airports that occurred in Asia is the closest to
38%
In the following table, individuals are cross-classified by their age group and income level. CHART For the chi-square test of independence, the degrees of freedom are
4
According to a study by the centers for disease control and prevention, about 33% of U.S. births are caesarean deliveries. suppose seven expectant mothers are randomly selected. the expected number of mothers who will not have a caesarean delivery is
4.69
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. (CHART) How many statistics classes had three or more students absent?
43
The likelihood of Company A's stock price rising is 20%, and the likelihood of Company B's stock price rising is 30%. Assume that the returns of Company A and Company B stock are independent of each other. The probability that the stock price of at least one of the companies will rise is
44%
the likelihood of a company As stock price rising is 20%
44%
the likelihood of company A's stock price rising is 20%, and the likelihood of company B's stock price rising is 30%. A and Company B are independent of each other. the probability that the stock price of at least one of the
44%
5! is equal to
5 × 4 × 3 × 2 × 1
Sarah's portfolio has an expected annual return at 8%, with an annual standard deviation at 12%. If her investment returns are normally distributed, then in any given year Sarah has an approximate ______.
50% chance that the actual return will be greater than 8%
The daily revenue from the sale of fried dough at a local street vendor in Boston is known to be normally distributed with a known standard deviation of $120. The revenue on each of the last 25 days is noted, and the average is computed as $550. Construct a 95% confidence interval for the population mean of the sale of fried dough by this vendor.
550 ± 1.96(120/5)
Suppose Bank of America would like to investigate if the credit score and income level of an individual are independent of one another. Bank of America selected a random sample of 400 adults and asked them to report their credit score range and their income range. The following contingency table presents these results. CHART The degrees of freedom for the critical value is
6
The following table shows the distribution of employees in an organization. Martha Foreman, an analyst, wants to see if race has a bearing on the position a person holds with this company. CHART For the chi-square test for independence to be valid, Martha combines the seniorities Manager and Director. As a result, the degrees of freedom used are
6
Suppose Bank of America would like to investigate if the credit score and income level of an individual are independent of one another. Bank of America selected a random sample of 400 adults and asked them to report their credit score range and their income range. The following contingency table presents these results. CHART The expected number of individuals with income between $50,000 and $100,000 and a credit score less than 650 is
60.0
A sociologist wishes to study the relationship between happiness and age. He interviews 24 individuals and collects data on age and happiness, measured on a scale from 0 to 100. He estimates the following model: Happiness = β0+ β1Age + ε. The following table summarizes a portion of the regression results. CHART Which of the following is the estimate of Happiness for the person who is 65 years old?
75
The following is an incomplete ANOVA table. CHART For the within groups category, the degrees of freedom are
8
AutoTrader.com would like to test if a difference exists in the age of three different types of vehicles currently on the road: trucks, cars, and vans. The following data represent the age of a random sample of trucks, cars, and vans. CHART The grand mean for these observations is
8.0
The mean grade of the 30 students in Section 1 is 80. The mean grade of the 40 students in Section 2 is 85. The mean grade of the 30 students in Section 3 is 80. What is the mean grade of all students from the three sections combined?
82.00
For any normally distributed random variable with mean μ and standard deviation σ, the percent of the observations that fall between [μ − 2σ, μ + 2σ] is the closest to ______.
95%
You work in marketing for a company that produces work boots. Quality control has sent you a memo detailing the length of time before the boots wear out under heavy use. They find that the boots wear out in an average of 208 days, but the exact amount of time varies, following a normal distribution with a standard deviation of 14 days. For an upcoming ad campaign, you need to know the percent of the pairs that last longer than six months—that is, 180 days. Use the empirical rule to approximate this percent.
97.5%
Consider the following cumulative distribution function for the discrete randomvarieble X 1 2 3 4 p(x<_x) 0.30 0.44 0.72 1.00 what is the probability that x equals 2?
??(not.44)
What may NOT be revealed from a scatterplot?
A causal relationship between two variables
Which of the following is correct?
A continuous random variable has a probability density function, and a discrete random variable has a probability mass function.
Which of the following relationships cannot be concluded from examining the correlation coefficient?
A curvilinear relationship
Statisticians like precision in their interval estimates. A low margin of error is needed to achieve this. Which of the following supports this when selecting sample sizes?
A larger sample size reduces the margin of error.
A particular personal trainer works primarily with track and field athletes. She believes that her clients run faster after going through her program for six weeks. How might she test that claim?
A matched-pairs hypothesis test for μD.
Which of the following meets the requirements of a cluster sample?
A population can be divided into 50 city blocks. The sample will include residents from two randomly chosen city blocks.
Which of the following meets the requirements of a simple random sample?
A population contains 10 members under the age of 25 and 20 members over the age of 25. The sample will include six people chosen at random, without regard to age.
Which of the following meets the requirements of a stratified random sample?
A population contains 10 members under the age of 25 and 20 members over the age of 25. The sample will include two people chosen at random under the age of 25 and four people chosen at random over 25.
What type of relationship is indicated in the scatterplot?
A positive linear or curvilinear relationship
When interpreting the covariance between variables x and y, which of the following statements is the most accurate?
A positive value of covariance indicates that, on average, if x is above its mean, then y tends to be above its mean.
Which of the following methods best describe the relationship between two categorical variables?
A stacked column chart
Which of the following is true about statistics such as the sample mean or sample proportion?
A statistic is a random variable.
What type of test for population means should be performed when employees are first tested, trained, and then retested?
A t test under dependent sampling.
What is probability?
A value between 0 and 1 assigned to an event that measures the likelihood of its occurrence.
Which of the following statements is most accurate when defining percentiles?
Approximately (100 − p)% of the observations are greater than the pth percentile.
Which of the following is the most influenced by outliers?
Arithmetic mean
A manager at a local bank analyzed the relationship between monthly salary (y, in $) and length of service (x, measured in months) for 30 employees. She estimates the following model: Salary = β0 + β1 Service + ε. The following table summarizes a portion of the regression results. CHART Using the 95% confidence interval, which of the following is the conclusion to the following hypothesis test: H0:β0 = 0; HA: β0 ≠ 0?
At the 5% significance level, reject H0 because the interval does not contain 0.
Suppose you want to determine if gender and major are independent. Which of the following tests should you use?
Chi-square test for independence
Which of the following is an example about analyzing the difference between two population means?
Compare the average six-year graduation rate between private and public colleges.
Which of the following is NOT an example of analyzing the mean difference of two populations based on matched-pairs sampling?
Compare the mean wait time of customers being served at a bank before and after the weekend.
An analyst takes a random sample of 25 firms in the telecommunications industry and constructs a confidence interval for the mean return for the prior year. Holding all else constant, if he increased the sample size to 30 firms, how are the standard error of the mean and the width of the confidence interval affected?
D ( decreases, becomes narrower)
Consider the sample regression equation yˆy^ = 12 + 3x1 − 5x2 + 7x3 − 2x4. When x1 increases by 1 unit and x2increases by 2 units, while x3 and x4 remain unchanged, what change would you expect in the predicted y?
Decrease by 7
What type of data is required to compare prices of the same textbooks sold by two different vendors?
Dependent random samples with numerical data.
If a population is known to be normally distributed, what can be said of the sampling distribution of the sample mean drawn from this population?
For any sample size n, the sampling distribution of the sample mean is normally distributed.
Which of the following statements is TRUE about goodness-of-fit measures
Goodness-of-fit measures are used to assess how well the explanatory variables explain the variation in the response variable.
In the following table, individuals are cross-classified by their age group and income level. CHART To test that age group and income are independent, the null and alternative hypothesis are
H0: Age group and income are independent; HA: Age group and income are dependent
In the following table, likely voters' preferences of two candidates are cross-classified by gender. CHART male 150, 100 female 130, 120 To test that gender and candidate preference are independent, the null hypothesis is
H0: Gender and candidate preference are independent
The following table shows the distribution of employees in an organization. Martha Foreman, an analyst, wants to see if race has a bearing on the position a person holds with this company. CHART To test that race and seniority are independent, the null and alternative hypothesis are
H0: Race and seniority are independent; HA: Race and seniority are dependent
A 7,000-seat theater is interested in determining whether there is a difference in attendance between shows on Tuesday evening and those on Wednesday evening. A random sample of 25 weeks is collected for Tuesday; a different sample of 25 weeks is collected for Wednesday. The mean attendance on Tuesday evening is calculated as 5,500, while the mean attendance on Wednesday evening is calculated as 5,850. The known population standard deviation for attendance on Tuesday evening is 550 and the known population standard deviation for attendance on Wednesday evening is 445. Let μ1 be the population mean of Tuesday, μ2 be the population mean of Wednesday, and μD be the mean difference for a matched-pairs sampling. What are the appropriate hypotheses to determine whether there is a difference, on average, in attendance between shows on Tuesday evening and Wednesday evening?
H0: µ1 − µ2 = 0, HA: µ1 − µ2 ≠ 0
A farmer uses a lot of fertilizer to grow his crops. The farmer's manager thinks fertilizer products from distributor A contain more of the nitrogen that his plants need than distributor B's fertilizer does. He takes two independent samples of four batches of fertilizer from each distributor and measures the amount of nitrogen in each batch. Fertilizer from distributor A contained 23 pounds per batch and fertilizer from distributor B contained 18 pounds per batch. Suppose the population standard deviation for distributor A and distributor B is four pounds per batch and five pounds per batch, respectively. Assume the distribution of nitrogen in fertilizer is normally distributed. Let µ1 and µ2 represent the average amount of nitrogen per batch for fertilizer's A and B, respectively. Specify the competing hypotheses to determine if fertilizer A contains more nitrogen per batch than fertilizer B.
H0: µ1 − µ2 ≤ 0, HA: µ1 − µ2 > 0
A bank is trying to determine which model of safe to install. The bank manager believes that each model is equally resistant to safe crackers but sets up a test to be sure. He hires nine safe experts to break into each of the models, timing each endeavor. The results (in seconds) are given next, paired by expert. Let D be the difference: Time to break Safe 1 minus Time to break Safe 2. Which of the following hypotheses will determine if the two safes take, on average, the same amount of time to crack?
H0: µD = 0, HA: µD ≠ 0
A farmer is concerned that a change in fertilizer to an organic variant might change his crop yield. He subdivides his six lots and uses the old fertilizer on one half of each lot and the new fertilizer on the other half. The following table shows the results. Which of the following are the appropriate competing hypotheses?
H0: µD = 0, HA: µD ≠ 0
A tutor promises to improve GMAT scores of students by more than 50 points after three lessons. To see if this is true, the tutor takes a sample of 49 students' test scores after and before they received tutoring. The mean difference was 53 points better after tutoring, with a standard deviation of the difference equal to 12 points. Let µD denote the mean of the difference: score after tutoring minus score before tutoring. Which of the following hypotheses will determine if the students improved their test scores by more than 50 points after being tutored?
H0: µD ≤ 50, HA: µD > 50
