BUS 204 Week 12 Assignment

BUS 204  Week 12  Assignment | MiraCosta College

1.

In the simple linear regression problem in the lecture videos, what is the COEFFICIENT of the SLOPE (for the store size in square feet)? Round your answer to two decimal places.  25.32

2.

federal law requires periodic testing in standard subjects. A random sample of

66

junior high school students from a certain city was selected, and each student's scores on a standardized mathematics examination and a standardized English examination were recorded. School administrators were interested in the relationship between the two scores. Suppose the correlation coefficient for the two examination scores is

0.74.

Complete parts a and b below. Use

α=0.05

where needed.

a. Provide an explanation of the sample correlation coefficient in this context. Fill in the blank below.

There appears to be

a fairly strong positive

 

correlation between the standardized mathematics examination and the standardized English examination for these students.

b. Using a level of significance of

α=0.05,

test to determine whether there is a positive linear relationship between mathematics scores and English scores for junior high school students in the city. What are the appropriate null and alternative hypotheses to test for a positive linear relationship?

 

A.

H0:

ρ≤0

HA:

ρ>0

Your answer is correct.

 

B.

H0:

ρ=0

HA:

ρ≠0

 

C.

H0:

ρ≠0

HA:

ρ=0

 

D.

H0:

ρ<0

HA:

ρ≥0

 

E.

H0:

ρ≥0

HA:

ρ<0

 

F.

H0:

ρ>0

HA:

ρ≤0

Calculate the t-test statistic for correlation.

t=

Determine the the rejection region for the test statistic t. Select the correct choice below and fill in the answer box(es) to complete your choice.

(Round to three decimal places as needed.)

 

A.

If

t<−t0.05= nothing,

reject the null hypothesis. Otherwise, do not reject the null hypothesis.

 

B.

If

t<−t0.025= nothing

or

t>t0.025= nothing,

reject the null hypothesis. Otherwise, do not reject the null hypothesis.

 

C.

If

t>t0.05= 1.6691.669,

reject the null hypothesis. Otherwise, do not reject the null hypothesis.

Your answer is correct.

Since the test statistic

is

 

in the rejection region,

reject

 

the null hypothesis. The data

do

 

support the contention that there is a

positive linear relationship

between the standardized mathematics examination and the standardized English examination.

 

3.

A regional retailer would like to determine if the variation in average monthly store sales can, in part, be explained by the size of the store measured in square feet. A random sample of

21

stores was selected and the store size and average monthly sales were computed. The results are shown in the accompanying table. Complete parts a through c below. Use a

0.005

significance level where needed.

 

Click the icon to view store size and average monthly sales data.

 

a. Construct a scatter plot using these data. What, if any relationship, appears to exist between the two variables?

Construct a scatter plot using these data. Choose the correct graph below.

 

Click here to view the scatter plot b.

LOADING...

Your answer is correct.

 

Click here to view the scatter plot d.

LOADING...

 

Click here to view the scatter plot c.

LOADING...

 

Click here to view the scatter plot a.

LOADING...

Based on the scatter plot,

a positive linear

 

relationship appears to exist between the two variables.

b. Calculate the sample correlation coefficient between store size and average monthly sales.

The correlation coefficient is

c. Conduct a hypothesis test to determine if a

positive

correlation exists between store size and average monthly sales. Use a level of significance of

0.005.

Identify the null and alternative hypotheses.

H0:

ρ

less than or equals≤

 00

HA:

ρ

greater than>

 00

(Type integers or decimals. Do not round.)

Identify the test statistic.

t= 7.667.66

Identify the rejection region and decision rule. Select the correct choice below and fill in the answer box(es) to complete your choice.

 

A.

If

t> 2.862.86,

reject

H0.

Otherwise, do not reject

H0.

Your answer is correct.

 

B.

If

 nothing<t< nothing,

reject

H0.

Otherwise, do not reject

H0.

 

C.

If

t< nothing,

reject

H0.

Otherwise, do not reject

H0.

 

D.

If

t> nothing

or if

t< nothing,

reject

H0.

Otherwise, do not reject

H0.

Reject

 

the null hypothesis. The sample data

support

 

the contention that a

positive

correlation exists between store size and average monthly sales.

 

4.

A business recently did a study of its customers. A random sample of

50

customer accounts was pulled from the computer records, and two variables were observed. The variable y is the total dollar volume of business this year, and x is the number of miles the customer is from corporate headquarters. The statistics shown to the right were computed.                     <="" path="">y =             2,139.46−9.79x

                                sb1         =             2.42

                                                               

                                                               

                                                               

                a.            Interpret the regression slope coefficient.

                b.            Using a significance level of

0.05,

test to determine whether it is true that the farther a customer is from the corporate headquarters, the smaller the total dollar volume of business.

a. Which statement below best interprets the regression slope coefficient?

 

A.

For each additional mile a customer is from the corporate headquarters, the average total dollar volume of business for the year increases by

$2,139.46.

 

B.

For each additional mile a customer is from the corporate headquarters, the average total dollar volume of business for the year decreases by

$2,139.46.

 

C.

For each additional mile a customer is from the corporate headquarters, the average total dollar volume of business for the year decreases by

$9.79.

 

D.

For each additional mile a customer is from the corporate headquarters, the average total dollar volume of business for the year increases by

$9.79.

b. What are the appropriate hypotheses to test?

 

A.

H0:

β1=0

HA:

β1≠0

 

B.

H0:

β1≤0

HA:

β1>0

 

C.

H0:

β1≥0

HA:

β1<0

 

5.

A regional retailer would like to determine if the variation in average monthly store sales can, in part, be explained by the size of the store measured in square feet. A random sample of

21

stores was selected and the store size and average monthly sales were computed. Complete parts a through c. Use a significance level of

0.10

where needed.

 

Click the icon to view the data table between the store size and average monthly sales.

 

a. Compute the simple linear regression model using the sample data to determine whether variation in average monthly sales can be explained by store size. What is the linear regression model based on the sample data?

<="" path="">y= 183778.44183778.44+( 24.6524.65)x

(Type integers or decimals rounded to two decimal places as needed.)

Interpret the slope coefficient. Select the correct choice below and fill in the answer box to complete your choice.

(Type an integer or decimal rounded to two decimal places as needed.)

 

A.

For each additional square foot of store size, the average increase in monthly sales is

$ 24.6524.65.

 

B.

For each additional dollar of monthly sales, the average increase in stores size is

 nothing

square feet.

Interpret the intercept coefficient. Select the correct choice below and fill in the answer box to complete your choice.

(Type an integer or decimal rounded to two decimal places as needed.)

 

A.

The average monthly sales of a store with 0 square feet is

$ nothing.

 

B.

The size of a store with average monthly sales of $0 is

 nothing

square feet.

 

C.

A store with no floor space cannot occur; therefore, the y intercept does not have a meaningful interpretation.

b. Test the significance of the slope coefficient of the regression model. Use a significance level of

0.10.

What are the appropriate hypotheses to test?

 

A.

H0:

β1<0

HA:

β1≥0

 

B.

H0:

β1>0

HA:

β1≤0

 

C.

H0:

β1≠0

HA:

β1=0

 

D.

H0:

β1≤0

HA:

β1>0

 

E.

H0:

β1=0

HA:

β1≠0

 

F.

H0:

β1≥0

HA:

β1<0

Determine the rejection region for the test statistic t. Select the correct choice below and fill in any answer boxes to complete your choice.

(Type integers or decimals rounded to three decimal places as needed.)

 

A.

t< nothing

 

B.

t> nothing

 

C.

t< negative 1.729−1.729

or

t> 1.7291.729

Your answer is correct.

Calculate the simple linear regression test statistic t.

t= 6.6536.653

(Type an integer or decimal rounded to three decimal places as needed.)

Since the test statistic

is

 

in the rejection region,

reject

 

the null hypothesis. Conclude that the regression model

is

 

significant. This means that knowing x

provides

 

useful help in predicting y.

c. Based on the estimated regression model, what percentage of the total variation in average monthly sales can be explained by store size?

 70.070.0%

(Type an integer or decimal rounded to one decimal place as needed.)

 

6.

The following data have been collected by an accountant who is performing an audit of paper products at a large office supply company. The dependent variable, y, is the time taken (in minutes) by the accountant to count the units. The independent variable, x, is the number of units on the computer inventory record. Complete parts a through c. Use a

90%

confidence level where needed.

x              23           126         217         42           181         16           89           170         40           118         235                        

y              21.5        99.3        248.3     53.6        177.5     11.8        95.8        206.4     40.3        125.4     161.6                    

a. Develop a scatter plot for these data. Choose the correct scatter plot below.

 

A.

02500260xy

•            

•            

•            

A set of coordinate axes with a horizontal axis titled x that ranges from 0 to 250 in increments of 25 and a vertical axis titled y that ranges from 0 to 260 in increments of 26. The following points are plotted: (25,20), (125,250), (215,100), (40,55), (180,10), (15,180), (90,95), (170,40), (40,205), (120,160), (235,125). All coordinates are approximate.

 

B.

02500260xy

•            

•            

•            

A set of coordinate axes with a horizontal axis titled x that ranges from 0 to 250 in increments of 25 and a vertical axis titled y that ranges from 0 to 260 in increments of 26. The following points are plotted: (25,20), (125,100), (215,250), (40,55), (180,180), (15,10), (90,95), (170,205), (40,40), (120,125), (235,160). All coordinates are approximate.

Your answer is correct.

 

C.

0120260xy

•            

•            

•            

A set of coordinate axes with a horizontal axis titled x that ranges from 0 to 12 in increments of 1 and a vertical axis titled y that ranges from 0 to 260 in increments of 26. The following points are plotted: (1,20), (2,100), (3,250), (4,55), (5,180), (6,10), (7,95), (8,205), (9,40), (10,125), (11,160). All coordinates are approximate.

 

D.

02500260xy

•            

•            

•            

A set of coordinate axes with a horizontal axis titled x that ranges from 0 to 250 in increments of 25 and a vertical axis titled y that ranges from 0 to 260 in increments of 26. The following points are plotted: (20,25), (100,125), (250,215), (55,40), (180,180), (10,15), (95,90), (205,170), (40,40), (125,120), (160,235). All coordinates are approximate.

b. Determine the regression equation representing the data. Is the model significant? Test using a significance level of

0.10

and the p-value approach.

The regression equation is

<="" path="">y= 7.08+ 0.93x.

(Round to two decimal places as needed.)

Determine the null and alternative hypotheses for the test. Choose the correct answer below.

 

A.

H0:

β1≠0

HA:

β1=0

 

B.

H0:

β1=0

HA:

β1>0

 

C.

H0:

β1>0

HA:

β1=0

 

D.

H0:

β1=0

HA:

β1≠0

 

E.

H0:

β1=0

HA:

β1<0

 

F.

H0:

β1<0

HA:

β1=0

Find the value of the test statistic.

t=

 

Find the p-value.

What is the conclusion for this test?

The p-value is

less than

 

0.10,

so

reject

 

the null hypothesis. There is

sufficient

 

evidence that the model is significant.

c. Develop a

90%

confidence interval estimate for the true regression slope and interpret this interval estimate. Based on this interval, could you conclude the accountant takes an additional minute to count each additional unit?

The

90%

confidence interval is

Interpret this interval estimate. Choose the correct answer below.

 

A.

For a one-unit decrease in y, x will decrease by an average of between the lower and upper limits of the confidence interval.

 

B.

For a one-unit increase in x, y will increase by an average of between the lower and upper limits of the confidence interval.

Your answer is correct.

 

C.

For a one-unit increase in y, x will decrease by an average of between the lower and upper limits of the confidence interval.

 

D.

For a one-unit decrease in x, y will increase by an average of between the lower and upper limits of the confidence interval.

Based on this interval, could you conclude the accountant takes an additional minute to count each additional unit?

 

A.

Since 1 lies does not lie within the

90%

confidence interval, it is possible to conclude that the accountant takes 1 more minute to count each additional unit, however the actual time may have a value anywhere between the two bounds of the confidence interval.

 

B.

Since 1 lies does not lie within the

90%

confidence interval, one cannot conclude that the accountant takes one minute to count each additional unit.