QMB FINAL
As the test statistic becomes larger, the p-value:
becomes smaller
When the level of confidence decreases, the margin of error
becomes smaller
Using an α = .04, a confidence interval for a population proportion is determined to be .65 to .75. If the level of significance is decreased, the interval for the population proportion:
becomes wider
The p-value
must be a number between 0 and 1
For a fixed sample size, n, in order to have a higher degree of confidence, the margin of error and the width of the interval:
must be larger
As a rule of thumb, the sampling distribution of the sample proportion can be approximated by a normal probability distribution when:
n(1 - p) ≥ 5 and np ≥ 5.
For the case where σ is unknown, the test statistic has a t distribution. How many degrees of freedom does it have?
n-1
When constructing a confidence or a prediction interval to quantify the relationship between two quantitative variables, the appropriate degrees of freedom are
n-2
When developing an interval estimate for the difference between two sample means, with sample sizes of n1 and n2 :
n1 and n2 can be of different sizes
Influential observations always:
none of the above are correct
The parameters of nonlinear models have exponents
other than one.
When completing a two-tailed hypothesis test about the difference between two population means, the
p-value must be doubled.
The sampling distribution of is the:
probability distribution of all possible values of the sample proportion.
Module 3
...
What is the probability of making a Type I error?
𝛼 alpha.
In multiple regression analysis, any observation with a standardized residual of less than _____ or greater than _____ is known as an outlier
-2;2.
In a multiple regression model, the error term ε is assumed to have a mean of:
0
The tests of significance in regression analysis are based on assumptions about the error term ɛ. One such assumption is that the error term ɛ is a random variable with a mean or expected value of:
0
The range of the Durbin-Watson statistic is
0 to 4.
When computing the sample size needed to estimate a proportion within a given margin of error for a specific confidence level, what planning value of p should be used when no estimate of p is available?
0.50
Multicollinearity can cause problems if the absolute value of the sample correlation coefficient exceeds
0.7 for any two of the independent variables
When dealing with the problem of nonconstant variance, we can apply the reciprocal transformation, which means that we use:
1/y as the dependent variable instead of y.
In an interval estimation for a proportion of a population, the critical value of z at 99% confidence is
2.576.
The z value for a 99% confidence interval estimation is:
2.58
The t value for a 99% confidence interval estimation based upon a sample of size 10 is:
3.250
In a multiple regression model, the values of the error term, ε, are assumed to be
: Independent of each other
The method used to develop the estimated regression equation that minimizes the sum of squared residuals is called the
: least squares method.
The regression model y=B0+B1x1+B2x2+B3x2^2+B4x2^2+B5x1x2+e is a
: second-order model with two predictor variables.
In a multiple regression model, the variance of the error term, ε, is assumed to be:
: the same for all values of x1, x2,..., xp..
To model a time series with a seasonal pattern, we treat the season as a(n):
Categorical variable.
The mathematical equation relating the expected value of the dependent variable to the value of the independent variables, which has the form of E(y)=B0+b1x1+b2x2+...+Bpxp, is called:
A multiple regression equation.
The mathematical equation that explains how the dependent variable y is related to several independent variables and has the form y=B0+b1x1+b2x2+....Bpxp+e is called:
A multiple regression model.
What kind of model is appropriate if the seasonal fluctuations change over time, growing larger as the dependent variable increases because of a long-term linear trend?
A multiplicative model
A statistics teacher started class one day by drawing the names of 10 students out of a hat and asked them to do as many pushups as they could. The 10 randomly selected students averaged 15 pushups per person with a standard deviation of 9 pushups. Suppose the distribution of the population of number of pushups that can be done is approximately normal. Which of the following statements is true?
A t distribution should be used because σ is unknown.
Which of the following scenarios follows a matched sample design?
A teacher uses a pretest and then a posttest with her students to see how much they have improved.
What kind of forecasting method is based on the assumption that the variable we are forecasting has a cause-effect relationship with one or more other variables?
Casual forecasting method.
Seasonal and irregular components with values greater than 1.00 indicate effects _____ the trend estimate and values below 1.00 indicate effects _____ the trend estimate. Which two words correctly complete this sentence
Above; below
Which of the following describes a Type II Error?
Accept H0 when H0 is false.
The time series model that is appropriate in situations where the seasonal fluctuations do not depend upon the level of the time series is
Additive model.
Which of the following exponential smoothing constant values puts the same weight on the most recent time series value as does a 5-period moving average?
Alpha = .2
The multiple regression equation based on the sample data, which has the form of y^ hat= b0+b1x1+b2x2+....+bpxp, is called:
An estimated multiple regression equation.
If the coefficient of determination is a positive value, then the coefficient of correlation:
Can be either negative or positive
Which of the following is not an iterative variable selection procedure?
Best-subsets regression
Which of the following options guarantees that the best model for a given number of variables will be found?
Best-subsets regression
The variable selection procedure that identifies the best regression equation, given a specified number of independent variables, is:
Best-subsets regression.
Whenever the probability of making a Type II error has not been determined and controlled, only two conclusions are possible. We either reject H0 or
Do not reject H0.
A variable used to model the effect of categorical independent variables is called a(n)
Dummy Variable
What test can be used to determine whether first-order autocorrelation is present?
Durbin-Watson test
Using the two-factorial design, write the form of the multiple regression equation that would give the expected value for level 1 of factor A and level 3 of factor B
E(y)=B0+b3
What forecasting method uses a weighted average of past time series values as the forecast; it is a special case of the weighted moving averages method in which we select only one weight—the weight for the most recent observation?
Exponential smoothing.
When using a weighted moving average, if we believe that the recent past is a better predictor of the future than the distant past, we should:
Give larger weights to recent observations
A local entrepreneur would like to know if those who live in a rural community are more likely to buy a real Christmas tree than those who live in an urban community. He takes a random sample of 100 people who reside in the city and a separate random sample of 100 people who live in the country and asks them if they buy a real tree at Christmas time. Of the urban participants, 22 buy a real tree. Of the rural participants, 28 buy a real tree. Let P1= the proportion of all people who live in rural communities and buy a real Christmas tree, and let P2 = the proportion of all people who live in urban communities and buy a real Christmas tree. State the null and alternative hypotheses.
H0: p1-p2<0, Ha:p1-p2>0
A student wants to determine if pennies are really fair, meaning equally likely to land heads up or tails up. He flips a random sample of 50 pennies and finds that 28 of them land heads up. What are the appropriate null and alternative hypotheses?
H0: p=.5, Ha:p not =.5.
It has been stated that at least 75 out of every 100 people who go to the movies on Saturday night buy popcorn. Identify the null and alternative hypotheses
H0: p>.75, Ha: p<.75.
Which of the following null hypotheses cannot be correct?
H0: u not=10.
A fast food restaurant has automatic drink dispensers to help fill orders more quickly. When the 12 ounce button is pressed, they would like for exactly 12 ounces of beverage to be dispensed. There is, however, undoubtedly some variation in this amount. The company does not want the machine to systematically over fill or under fill the cups. Which of the following gives the correct set of hypotheses?
H0: u=12, Ha: u not=12
A news reporter states that the average number of temperature in January has never dropped below 10 degrees Fahrenheit. You go online to research this claim. The appropriate hypotheses are:
H0: u>10, Ha: u<10.
A doctor would like to know if men and women got the same amount of sleep per night or if women tended to get less sleep than men. He took a random sample of 100 of his male and 100 of his female patients and asked them how many hours of sleep they got, per night, on average. The women slept an average of 6.75 hours and the men slept an average of 7.5 hours. Suppose we also knew the population standard deviations to be 1.25 hours and 1.5 hours for men and women, respectively. Formulate the null and alternative hypotheses to test whether women sleep less than men do, on average
H0:: Um-Um=0, Ha: Um-UW<0
The average hourly wage of computer programmers with 2 years of experience has been $21.80. Because of high demand for computer programmers, it is believed there has been a significant increase in the average wage of computer programmers. To test whether there has been an increase, the correct hypotheses to be tested are
H0:u<21.80, Ha: u>21.80.
The average number of hours for a random sample of mail order pharmacists from company A was 50.1 hours last year. It is believed that changes to medical insurance have led to a reduction in the average work week. To test the validity of this belief, the hypotheses are:
H0:u>50.1, Ha:u<50.1.
Time series decomposition can be used to separate or decompose a time series into all of the following components except:
Horizontal patterns
When we conduct significance tests for a multiple regression relationship, the t test can be conducted for each of the independent variables in the model. Each of those tests are called tests for:
Individual significance.
An observation that has a strong influence or effect on the regression results is called a(n):
Influential observation.
The effect of two independent variables acting together is called:
Interaction.
Which of the following statements about the backward elimination procedure is false
It begins with zero independent variables.
Which of these best describes a sampling distribution of a statistic?
It is the distribution of all of the statistics calculated from all possible samples of the same sample size.
Since the multiple regression equation generates a plane or surface, its graph is called a:
Response surface
If a categorical variable has k levels, then
K-1 dummy variables are needed
Larger values of r2 imply that the observations are more closely grouped about the
Least squares line.
Three of the following forecasting methods are appropriate for a time series with a horizontal pattern. Which one is not appropriate for a time series with a horizontal pattern?
Linear trend regression.
The tests of significance in regression analysis are based on several assumptions about the error term ɛ. Additionally, we make an assumption about the form of the relationship between x and y. We assume that the relationship between x and y is
Linear.
A company wants to identify which of the two production methods has the smaller completion time. One sample of workers is selected and each worker first uses one method and then uses the other method. The sampling procedure being used to collect completion time data is based on:
Matched samples.
The average of the absolute values of the forecast errors is called:
Mean absolute error
The method that uses the average of the most recent k data values in the time series as the forecast for the next period is called
Moving averages.
The proportion of the variability in the dependent variable that can be explained by the estimated multiple regression equation is called the:
Multiple coefficient of determination
When we conduct significance tests for a multiple regression relationship, the F test will be used as the test for
Overall significance
The sampling distribution of P1-P2 is approximated by a normal distribution when:
N1P1,N1(1-P1), N2P2, and N2(1-P2) are all greater than or equal to 5.
The sampling distribution of is approximated by a
Normal distribution.
A graph of the standardized residuals plotted against values of the normal scores that helps to determine whether the assumption that the error term has a normal probability distribution appears to be valid is called a:
Normal probability plot
In a multiple regression model, the values of the error term, ε, are assumed to be:
Normally distributed
Which of the following is not present in a time series?
Operational variations
All things held constant, which interval will be wider: a confidence interval or a prediction interval?
Prediction interval
A forecast model of the form is called a(n):
Quadratic trend equation.
When historical data on the variable being forecast are either not applicable or unavailable, what kind of forecasting method should be used
Qualitative methods
In best-subsets regression, Minitab can be used to provide output that identifies the two best one-variable estimated regression equations, the two best two-variable estimated regression equations, the two best three-variable estimated regression equations, and so on. What criterion is used in determining which estimated regression equations are best
R^2
Which of the following statements is false?
Regression analysis can be interpreted as a procedure for establishing a cause-and-effect relationship between variables.
In regression analysis, the equation in the form y = 𝛽0 + 𝛽1x + ε is called the:
Regression model.
Which of the following describes a Type I Error?
Reject H0 when H0 is true.
For the case where σ is unknown, which statistic is used to estimate σ?
S
Which of the following is a point estimator?
S.
Which of the following is not a symbol for a parameter?
S.
The regression model y=B0+B1x1+B2x1^2+e is a:
Second-order model with one predictor variable.
An F test, based on the F probability distribution, can be used to test for
Significance in regression.
The Durbin-Watson test is generally inconclusive for:
Smaller sample sizes
The average of all the historical data will always provide the best results as long as the underlying time series is:
Stationary
When determining the best estimated regression equation to model a set of data, the procedure that begins each step by determining whether any of the variables already in the model should be removed is called:
Stepwise regression
What is the component of a time series model that is attributable to multiyear cycles in the time series?
The cyclical component
When autocorrelation is present, which of the following assumptions is violated?
The error terms are independent.
When carrying out an F test to determine if the addition of extra predictor variables results in a significant reduction in the error sum of squares, what are the degrees of freedom of the numerator and denominator of the F statistic?
The numerator degrees of freedom equals the number of predictors added to the model. The denominator degrees of freedom is n—p—1.
The standard error of is given by:
The one that has a root square covering the entire thing
Which of the following does not need to be known in order to compute the p-value?
The level of significance.
Write a multiple regression equation that can be used to analyze the data for a two-factorial design with two levels for factor A and four levels for factor B
The longest one that ends with 1 and 4
As the number of degrees of freedom for a t distribution increases, the difference between the t distribution and the standard normal distribution
becomes smaller
Suppose sales data for the first quarter had a seasonal index of .80. Which of the following statements correctly interprets this figure?
The sales average is 20% below the trend estimate.
The tests of significance in regression analysis are based on assumptions about the error term ɛ . One such assumption is that the variance of ɛ, denoted by 𝝈2, is
The same for all values of x.
Which of the following statements regarding the sampling distribution of sample means is incorrect?
The standard deviation of the sampling distribution is the standard deviation of the population.
In a regression analysis, an outlier will always increase:
The value of the correlation.
What type of analysis aims to discover a pattern in the historical data or time series and then extrapolate the pattern into the future?
Time series analysis
A time series method that is used to separate or decompose a time series into seasonal, trend, and irregular components is called
Time series decomposition.
The sample mean is the point estimator of:
U
A positive forecast error indicates that the forecasting method _____ the dependent variable.
Underestimated.
Dummy variables must always have:
Values of either 0 or 1
What is the symbol for the sample mean?
X bar
IN the linear trend equation, Tt = b0 + b1t, b0 represents the
Y-intercept of the trend line.
What forecasting method involves selecting a different weight for the most recent k data values in the time series and then computing a weighted average of the values?
Weighted moving average method.
Which of the following set of circumstances is not needed to carry out quantitative forecasting methods?
When the historical data has a correlation of 1
In interval estimation, as the sample size becomes larger, the interval estimate:
becomes narrower
With negative autocorrelation, we expect a positive residual in one period to be followed by:
a negative residual in the next period, then a positive residual, and so on.
cluster sampling is
a probability sampling method
If we are interested in testing whether the proportion of items in population 1 is larger than the proportion of items in population 2, then the:
alternative hypothesis should state.
The following linear trend expression was estimated using a time series with 9 years as the independent variable and annual profit as the response variable (in millions). Tt = 29.2 + 3.8t. The value 3.8 represents the:
amount that the profit is expected to increase by each year, in millions of dollars, on average.
When working with regression analysis, an outlier is:
any observation that does not fit the trend shown by the remaining data.
An approximate value of a population parameter that provides limits and believed to contain the value of the parameter is known
as the interval estimate
Suppose a residual plot of x verses the residuals, y - ŷ, shows a nonconstant variance. In particular, as the values of x increase, suppose that the values of the residuals also increase. This means that:
as the values of x get larger, the ability to predict y becomes less accurate.
For a lower tail test, the p-value is the probability of obtaining a value for the test statistic:
at least as small as that provided by the sample.
Correlation in the errors that arises when the error terms at successive points in time are related is called:
autocorrelation.
If two large independent random samples are taken from two populations, the sampling distribution of the difference between the two sample means:
can be approximated by a normal distribution.
The value of the coefficient of correlation (r):
can be equal to the value of the coefficient of determination (r2).
In multiple regression analysis, the general linear model:
can be used to accommodate curvilinear relationships between the independent variables and the dependent variable.
The coefficient of determination:
cannot be negative
The fact that the sampling distribution of sample means can be approximated by a normal probability distribution whenever the sample size becomes large is based on the:
central limit theorem.
When studying the relationship between two quantitative variables, an interval estimate of the mean value of y for a given value of x is called a(n):
confidence interval.
When we use the estimated regression equation to develop an interval that can be used to predict the mean for ALL units that meet a particular set of given criteria, that interval is called a(n):
confidence interval.
As the sample size increases, the margin of error:
decrease
Suppose we are constructing an interval estimate for the difference between the means of two populations when the standard deviations of the two populations are unknown. Suppose it can be assumed that the two populations have equal variances. If n1 is the size of sample 1 and n2 is the size of sample 2, we must use a t distribution with:
degrees of freedom.
In regression analysis, the variable that is being predicted is the:
dependent variable
A time series from which the effect of season has been removed by dividing each original time series observation by the corresponding seasonal index is called a:
deseasonalized time series.
A simple random sample of size n from an infinite population is a sample selected such that:
each element is selected independently and is selected from the same population.
The term in the multiple regression model that accounts for the variability in y that cannot be explained by the linear effect of the p independent variables is the:
error term
If a significant relationship exists between x and y and the coefficient of determination shows that the fit is good, the estimated regression equation should be useful for:
estimation and prediction
What is the symbol for the population mean? If the population follows a normal distribution, the confidence interval is _____ and can be used for any sample size. If the population does not follow a normal distribution, the confidence interval will be _____. Which of the following choices correctly complete this statement?
exact; approximate
If the value of y in time period t is related to its value in time period t - 1, we say that
first-order autocorrelation is present.
The difference between the actual time series value and the forecast is called:
forecast error.
For a fixed confidence level and population standard deviation, if we would like to cut our margin of error in half, we should take a sample size that is
four times as large as the original sample size.
Which of the following variables is categorical?
gender
A model in the form of , where each independent variable zj (for j = 1, 2,..., p) is a function of x1, x2,..., xk, is known as the:
general linear model.
Looking at the sample correlation coefficients between the response variable and each of the independent variables can give us a quick indication of which independent variables are, by themselves,
good predictors
Observations with extreme values for the independent variables are called
high leverage points.
The central limit theorem states that:
if the sample size n is large, then the sampling distribution of the sample mean can be approximated by a normal distribution.
One way to have high confidence and a small margin of error is to:
increase the sample size
In general, R2 always _____ as independent variables are added to the regression model
increases
We can reduce the margin of error in an interval estimate of p by doing any of the following except
increasing the planning value p* to .5.
The tests of significance in regression analysis are based on assumptions about the error term ɛ. One such assumption is that the values of ɛ are:
independent
Regarding inferences about the difference between two population means, the alternative to the matched sample design, as covered in the textbook, is:
independent samples.
When using a categorical variable in a multiple regression model that has k levels, how many dummy variables are needed?
k - 1
The probability that the interval estimation procedure will generate an interval that does not contain µ is known as the
level of significance
The probability of making a Type I error when the null hypothesis is true as an equality is called the:
level of significance.
The value added and subtracted from a point estimate in order to develop an interval estimate of the population parameter is known as the:
margin of error
A researcher recruits 25 people to participate in a study on alcohol consumption and its interactions with Tylenol. The 25 participants had to come to a check-in center every day at 7:00 a.m. for one week. They were given various amounts of alcohol. Each day, each participant would flip a coin to determine if they also took Tylenol with their alcohol. They found that their BAC was 25% higher on days when they were given Tylenol with their alcohol than when they drank alcohol alone. This is an example of a(n):
matched sample design.
The average of the sum of squared forecast errors is called:
mean squared error.
The term used to describe the case when the independent variables in a multiple regression model are correlated is:
multicollinearity.
The study of how a dependent variable y is related to two or more independent variables is called:
multiple regression analysis.
For a fixed confidence level and population standard deviation, if we would like to cut our margin of error to 1/3 of the original size, we should take a sample size that is:
nine times as large as the original sample size.
The tests of significance in regression analysis are based on assumptions about the error term ɛ. One such assumption is that the error term follows ɛ a(n) _____ distribution for all values of x
normal
A sample of 92 observations is taken from an infinite population. The sampling distribution of is approximately:
normal because of the central limit theorem.
The sampling distribution of can be approximated by a normal distribution as long
np> 5 and n(1-p)>5 greater or equals.
The normal probability distribution can be used to approximate the sampling distribution of as long as:
np>5 and n(1-p)>5.
The p-value is a probability that measures the support (or lack of support) for the
null hypothesis
A seasonal pattern
occurs when a time series plot exhibits a repeating pattern over successive periods.
When we use the estimated regression equation to develop an interval that can be used to predict the mean for a specific unit that meets a particular set of given criteria, that interval is called a(n):
prediction
When studying the relationship between two quantitative variables, whenever we want to predict an individual value of y for a new observation corresponding to a given value of x, we should use a(n):
prediction interval
Doubling the size of the sample will:
reduce the standard error of the mean
The mathematical equation relating the independent variable to the expected value of the dependent variable, E(y)=B0+b1x, is known as the
regression equation.
The model developed from sample data that has the form y^hat=bo+b1x is known as the:
regression equation.
Graphical representation of the residuals that can be used to determine whether the assumptions made about the regression model appear to be valid is called a
residual plot
The difference between the observed value of the dependent variable and the value predicted using the estimated regression equation is called a(n):
residual.
When x is unknown, which of the following is used to estimate x? s Suppose we have a t distribution based upon two sample means with unknown population standard deviations, which we are unwilling to assume are equal. When we calculate the appropriate degrees of freedom, we should:
round the calculated degrees of freedom down to the nearest integer.
When "s" is used to estimate "σ," the margin of error is computed by using the: t distribution. The margin of error in an interval estimate of the population mean is a function of all of the following except the:
sample mean
The value of the _____ is used to estimate the value of the population parameter.
sample statistic
The probability distribution of all possible values of the sample proportion is the:
sampling distribution of p
The distribution of values taken by a statistic in all possible samples of the same size from the same population is called a:
sampling distribution.
If data for a time series analysis is collected on an annual basis only, which component may be ignored?
seasonal
Applications of hypothesis testing that only control for the Type I error are called:
significance tests.
When determining the best estimated regression equation to model a set of data, the procedure that allows an independent variable to enter the model at one step, be removed at a subsequent step, and then enter the model at a later step is
stepwise regression.
When constructing a confidence or a prediction interval to quantify the relationship between two quantitative variables, what distribution do confidence and prediction intervals follow?
t distribution
From a population that is normally distributed, a sample of 30 elements is selected and the standard deviation of the sample is computed. For the interval estimation of μ, the proper distribution to use is the:
t distribution with 29 degrees of freedom.
In most applications of the interval estimation and hypothesis testing procedures, random samples withn1 ≥ 30 and n2 ≥ 30 are adequate. In cases where either or both sample sizes are less than 30:
the distribution of the populations becomes an important consideration.
For the interval estimation of μ when σ is known and the sample is large, the proper distribution to use is:
the normal distribution
In hypothesis testing, the tentative assumption about the population parameter is called
the null hypothesis
If a residual plot of x versus the residuals, y - ŷ, shows a non-linear pattern, then we should conclude that
the regression model is not an adequate representation of the relationship between the variables.
A simple random sample of size n from an infinite population of size N is to be selected. Each possible sample should have:
the same probability of being selected
The distribution of values taken by a statistic in all possible samples of the same size from the same population is the sampling distribution of:
the sample
In multiple regression analysis:
there can be several independent variables, but only one dependent variable.
All of the following are true about qualitative forecasting methods except:
they assume that the pattern of the past will continue into the future.
In order to use the output from a multiple regression model to perform the ANOVA test on the difference among the means of four populations, how many dummy variables do we need to use to indicate treatments?
three
Time series regression refers to the use of regression analysis when the independent variable is:
time
If the historical data are restricted to past values of the variable to be forecast, the forecasting procedure is called a
time series method.
The time series component that reflects gradual variability over a long time period is called:
trend
What value of Durbin-Watson statistic indicates that no autocorrelation is present?
two
For a two-tailed test, the p-value is the probability of obtaining a value for the test statistic as:
unlikely as that provided by the sample.
To compute the necessary sample size for an interval estimate of a population proportion, all of the following procedures are recommended when p is unknown except
using .95 as an estimate
To compute the necessary sample size for an interval estimate of a population mean, all of the following procedures are recommended when σ is unknown except: .
using σ = 1.
The matched sample design often leads to a smaller sampling error than the independent sample design. The primary reason is that in a matched sample design:
variation between subjects is eliminated because the same subjects are used for both treatments.
Regarding hypothesis tests about , the pooled estimate of P is a
weighted average of P1 and P2.
The central limit theorem is important in Statistics because it: enables reasonably accurate probabilities to be determined for events involving the sample average
when the sample size is large regardless of the distribution of the variable.
Suppose a high correlation existed between variables x 1 and x 2 . If variable x 1 was used as an independent variable, then variable x 2 :
would not add much more explanatory power to the current model.
How many independent variables does the forward selection process start with?
zero
In a regression analysis, the error term ε is a random variable with a mean or expected value of
zero
The sample statistic characteristic s is the point estimator of:
σ..