BUS 245 exam 3

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which of the following sample correlation coefficients shows the strongest linear association between x and y?

-0.95

the sample coefficient value is between

-1 and 1

a test in which the null hypothesis is rejected only on one side of the hypothesized value of the population parameter

1 tailed test

a test in which the null hypothesis can be rejected on either side of the hypothesized value of the population parameter

2 tailed test

we do not reject the null hypothesis when the p-value is

>= a

y=Bo+B1x+E which symbol represents the intercept?

B0

y=Bo+B1x+E which symbol represents slope?

B1

a type II error occurs when we

Do not reject the null hypothesis when it is actually false

which symbol represents random error in the linear regression model? y=Bo+B1x+E

E

the alternative hypothesis for a one sided test look like:

Ha:u<u0

in a simple linear regression, a downward sloping trend line suggests which of the following?

a negative linear relationship between x and y

in a simple linear regression, an upward sloping trend line suggests which of the following?

a positive linear relationship between x and y

the significance level is the probability of making

a type 1 error

which of the following statements best defines a test statistic in a hypothesis test?

a variable upon which the decision in hypothesis testing is based

contradicts the default state or status quo specified in the null hypothesis

alternative hypothesis

the _________ _________ typically contests the status quo and may suggest a corrective action if true

alternative hypothesis

which of the following identifies the range for a correlation coefficient?

any value between -1 and 1, inclusive

which of the following is a possible advantage of using multiple tools to judge the validity of a regression model?

avoid the risk of using the wrong model

which of the following are the estimated model coefficients of the simple linear regression equation?

b0 and b1

In a simple linear regression model, which of the coefficients in the stilted sample regression equation indicates the cane in the predicted value of y when x increases by one unit?

b1

the coefficient of determination can assume which of the following values?

between zero and one

in practice, we use a stochastic model over a deterministic model because

certain variables that impact the response variable are not included in the model

an important final conclusion to a statistical test is to

clearly interpret the results in terms of the initial claim

the ____ Se is to 0, the better the model fits the data

closer

The goodness-of-fit measure that quantifies the proportion of the variation in the response variable that is explained by the sample regression equation is the

coefficient of determination

the proportion of the sample variation in the response variable that is explained by the sample regression equation

coefficient of determination

what does the goodness of fit measure?

coefficient of determination, adjusted coefficient or determination, standard error of the estimate

an alternative hypothesis

contradicts the status quo

what is the difference between correlation and causation?

correlation means that two variables are related, but causation means that one variable causes another to happen

this approach is used when a computer is not available and all calculations must be done by hand

critical value approach

matched pairs sampling is an example of

dependent sampling

in regression analysis, the response variable is also called the

dependent variable

when the response variable is uniquely determined by the explanatory variable, the relationship is

deterministic

unlike R^2, adjusted R^2 can be used to compare regression models with

different numbers os explanatory variables

one limitation of correlation analysis is that it

does not imply causation

a measure of degree of variability that exists even if all population means are the same; measures the unexplained variation in the response variable

error sum of squares (SSE)

we can generally reduce both type I and type II errors simultaneously by

increasing the sample size

two or more samples are _______ if the process that generates one sample is completely separate from the process that generates the other sample

independent

two or more random samples are considered independent if the process that generates one sample is completely separate from the other sample

independent random samples

in hypothesis tests about the population correlation coefficient, the alternative hypothesis of not equal to zero is used when testing whether two variables are

linearly related

a confidence interval for the mean difference ud follows the general format of a point estimate +-

margin of error

if the correlation between the response variable and the explanatory variables is sufficiently low, then adjusted R^2

may be negative

one limitation of correlation analysis is that it

may not be a reliable measure when outliers are present in one or both of the variables

For matched-pairs sampling, the parameter of interest is referred to as the

mean difference

allows us to examine how the response variability is influenced by two or more explanatory variables

multiple linear regression model

if the value of the sample covariance between the two random variables X and Y equals -150 then we can conclude that x and Y have a

negative linear relationship

a binomial distribution can be approximated by a _______ distribution for large sample sizes

normal

statistical inference concerning the difference in population means is based on one condition that the sampling distribution of x1-x2 follows a

normal distribution

when testing u, the p-value is the probability of obtaining a sample mean at least as large or at least as small as the one derived from a given sample, assuming the ___ hypothesis is true

null

corresponds to the presumed default state of nature or status quo

null hypothesis

the p-value is calculated assuming the

null hypothesis is true

what values can the standard of error of the estimate x assume?

o<= x< infinity

one limitation of correlation analysis is that it

only captures a linear relationship between two variables

a regression technique for fitting a straight line whereby the error sum of squares is minimized

ordinary least squares

name the mathematical method that produces the "best fitting trend line"

ordinary least squares

a few extreme high or low values in the data set are called

outliers

we can reject the null hypothesis when the

p-value < a

two approaches for a hypothesis test:

p-value and critical value approach

this approach is used by most researchers and practitioners; requires statistical software package

p-value approach

the two equivalent methods to solve a hypothesis test are the:

p-value approach and critical value approach

when comparing two population proportions, the parameter of interest is

p1-p2

hypothesis testing is used to resolve conflicts between 2 competing hypotheses on what?

particular parameter of interest

a pooled sample proportion can be computed when testing to see if two population proportions are equal. the pooled value represents an estimate of the unknown

population proportion

what type of relationship exists between two variables if as one increases, the other increases?

positive

if the value of the sample covariance between the two random variables x and y equals 14.67, we can conclude that x and y have a

positive linear relationship

unlike the mean and standard deviation, the population proportion p is a descriptive summary measure that can be used for data that are _______

qualitative

the difference between the observed and the predicted values of y

residual e

the standard error of the estimate is the standard deviation of the

residuals

the competing hypothesis Ho:p1-p2<=Do versus Ha:p1-p2>Do is a

right tailed test

when testing u and o is known, H0 can never be rejected if z<= 0 for a

right tailed test

in inferential statistics, we use ____________ information to make inferences about and unknown population parameter

sample

gauges the direction and strength of the linear relationship between two variables

sample correlation coefficient

the point estimate for the difference between two population means is represented by the difference between two:

sample means

measures the direction of the linear relationship

sample variance

numerical measure that gauges dispersion from the sample regression equation

sample variance of the residual

shows the relationship between two variables

scatterplot

the allowed probability of making a type I error (100a%)

significance level

in regression analysis one explanatory variable is used to explain the variability in the response variable

simple linear regression model

steps of p-value approach to hypothesis testing in order:

specify the null and alternative hypotheses, calculate the value of the test statistic and its p-value, state the conclusion and interpret the results

a numerical measure that gauges the dispersion of data points from the sample regression equation is referred to as the

standard error of the estimate

standard deviation of the residual; used as a goodness of fit measure for regressional analysis

standard error of the estimate

margin of error=

standard of error

when the value of the response variable is not uniquely determined by the explanatory variable, the relationship is said to be

stochastic

if r=0.83, we can conclude that x and y have a relatively

strong, positive linear relationship

sample-based measure used in hypothesis testing

test-statistic

the sample variance of the residual is defined as

the average of the squared differences between y1 and y^1

the residual e represents

the difference between an observed and predicted value of the response variable at a given value of the explanatory variable

the multiple regression model is used when?

the researcher believes that two or more explanatory variables influence the response variable

for which of the following situations is a simple linear regression model appropriate?

the response variable y is influenced by one explanatory variable

unlike R^2, adjusted R^2 explicitly accounts for

the sample size and the number of explanatory variables

statistical inference concerning the mean difference based on matched-pairs sampling requires one of two conditions. what are the two conditions?

the sample size n >=5 and both x1 and x2 are normally distributed

in evaluating a regression model, why is a scatterplot a useful tool?

the scatterplot can be used to asses the linearity of the relationship

SST represents what?

total variation in y

true or false: for a given sample size n, a type I error can only be reduced at the expense of a higher type II error

true

true or false: in a two-tailed test, we can reject the null hypothesis on either side of the hypothesized value of the population parameter

true

true or false: the optimal values of type I and type II errors require a compromise in balancing the costs of each type of error

true

true or false: we choose a value for a before conducting a hypothesis test

true

the hypothesis Ho:u1-u2=Do versos Ha:u1-u2 not=Do indicates

two tailed test

we specify the alternative hypothesis as Ha:p<0 when we want to test if

two variables are negatively linearly related

committed when we reject the null hypothesis and it is actually true

type I error

made when we do not reject the null hypothesis when the null hypothesis is actually false

type II error

we calculated a pooled estimate of the common variance by

using the weighted averages of the sample variances

if sample evidence is inconsistent with the null hypothesis=

we reject the null hypothesis

when conducting a hypothesis test, we determine

whether the sample data support the alternative hypothesis

y=Bo+B1x+E which symbol represents the explanatory variable?

x

what does the model y=Bo+B1x+E tell us about the relationship between the variables x and y?

x and y are linearly related, but the relationship is inexact or stochastic

which symbol represents the response variable in the linear regression model? y=Bo+B1x+E

y

in a simple linear regression model , if all of the data points fall on the sample regression line, then the standard error of the estimate is

zero

in most applications, the hypothesized difference between two population means is

zero

the hypothesized difference between 2 population means U1 and U2 is

zero


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