Exam 4-Business Statistics- questions
with complete solutions
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.
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.
- 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.
Which of the following are the competing hypotheses used to test whether
Advertising is significant in predicting Sales? - - 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.
When testing whether Advertising is significant at the 10% significance level,
the conclusion is to ________. - - reject H0; we can conclude advertising is
significant
- 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.
The degrees of freedom for the hypothesis test are _______. - - 3, 20
- 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.
The competing hypotheses about the mean commute times are _______. - -
H0: μ1 = μ2 = μ3 = μ4, HA: Not all population means are equal
- 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 regression equation is given by yˆy^ = −100 + 0.5x. If x = 20,
the predicted value of y is ________. - - -90
- Consider the following simple linear regression model: y = β0 + β1x + ε.
When determining whether x significantly influences y, the null hypothesis
takes the form ________. - - H0:β1 = 0
- Consider the following simple linear regression model: y = β0 + β1 + ε.
The response variable is ________. - - y
- Consider the following simple linear regression model: y = β0 + β1x + ε.
The explanatory variable is ________. - - x
- 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.
The grand mean for these observations is ________. - - 8.0
- 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
- 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
- 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
with complete solutions
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.
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.
- 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.
Which of the following are the competing hypotheses used to test whether
Advertising is significant in predicting Sales? - - 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.
When testing whether Advertising is significant at the 10% significance level,
the conclusion is to ________. - - reject H0; we can conclude advertising is
significant
- 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.
The degrees of freedom for the hypothesis test are _______. - - 3, 20
- 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.
The competing hypotheses about the mean commute times are _______. - -
H0: μ1 = μ2 = μ3 = μ4, HA: Not all population means are equal
- 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 regression equation is given by yˆy^ = −100 + 0.5x. If x = 20,
the predicted value of y is ________. - - -90
- Consider the following simple linear regression model: y = β0 + β1x + ε.
When determining whether x significantly influences y, the null hypothesis
takes the form ________. - - H0:β1 = 0
- Consider the following simple linear regression model: y = β0 + β1 + ε.
The response variable is ________. - - y
- Consider the following simple linear regression model: y = β0 + β1x + ε.
The explanatory variable is ________. - - x
- 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.
The grand mean for these observations is ________. - - 8.0
- 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
- 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
- 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
