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1

If we find that there is a linear correlation between the concentration of carbon dioxide in our atmosphere and the global temperature, does that indicate that changes in the concentration of carbon dioxide cause changes in the global temperature?

Choose the correct answer below.

A.

No. The presence of a linear correlation between two variables does not imply that one of the variables is the cause of the other variable.

B.

Yes. The presence of a linear correlation between two variables implies that one of the variables is the cause of the other variable.

2

For a sample of eight bears, researchers measured the distances around the bears’ chests and weighed the bears. Minitab was used to find that the value of the linear correlation coefficient is

requals=0.8830.883.

Using

alphaαequals=0.05,

determine if there is a linear correlation between chest size and weight. What proportion of the variation in weight can be explained by the linear relationship between weight and chest size?

Click here to view a table of critical values for the correlation coefficient.

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1. Is there a linear correlation between chest size and weight?

A.

Yes, because the absolute value of the test statistic exceeds the critical value

of 0.707of 0.707.

B.

Yes, because the test statistic falls between the critical values of

negative 0.707−0.707

and 0.707.

C.

No, because the absolute value of the test statistic exceeds the critical value

of 0.707of 0.707.

D.

The answer cannot be determined from the given information.

1. What proportion of the variation in weight can be explained by the linear relationship between weight and chest size?

(Round to three decimal places as needed.)

3

Use the given data set to complete parts (a) through (c) below. (Use

alphaαequals=0.05.)

LOADING…

Click here to view a table of critical values for the correlation coefficient.

1. Construct a scatterplot. Choose the correct graph below.

A.

04812160246810xy

A scatterplot has a horizontal x-scale from 0 to 16 in increments of 2 and a vertical y-scale from 0 to 10 in increments of 1. Eleven points are plotted with approximate coordinates as follows: (4, 2); (5, 2.6); (6, 3); (7, 3.6); (8, 4); (9, 4.6); (10, 5); (11, 5.6); (12, 6); (13, 6.6); (14, 7).

B.

04812160246810xy

A scatterplot has a horizontal x-scale from 0 to 16 in increments of 2 and a vertical y-scale from 0 to 10 in increments of 1. Eleven points are plotted with approximate coordinates as follows: (4, 1); (5, 1.4); (6, 1.6); (7, 2); (8, 2.4); (9, 3); (10, 3.6); (11, 4.2); (12, 4.8); (13, 6); (14, 8).

C.

04812160246810xy

A scatterplot has a horizontal x-scale from 0 to 16 in increments of 2 and a vertical y-scale from 0 to 10 in increments of 1. Eleven points are plotted with approximate coordinates as follows: (4, 6); (5, 5.6); (6, 5); (7, 4.6); (8, 4); (9, 3.6); (10, 3); (11, 2.6); (12, 2); (13, 1.6); (14, 1).

D.

04812160246810xy

A scatterplot has a horizontal x-scale from 0 to 16 in increments of 2 and a vertical y-scale from 0 to 10 in increments of 1. Eleven points are plotted with approximate coordinates as follows: (4, 3.2); (5, 4.8); (6, 6.2); (7, 7.2); (8, 8.2); (9, 8.8); (10, 9.2); (11, 9.2); (12, 9.2); (13, 8.8); (14, 8.2).

1. Find the linear correlation coefficient, r, then determine whether there is sufficient evidence to support the claim of a linear correlation between the two variables.

The linear correlation coefficient is

requals=

(Round to three decimal places as needed.)

Determine whether there is sufficient evidence to support the claim of a linear correlation between the two variables. Choose the correct answer below.

A.

There is

insufficientinsufficient

evidence to support the claim of a nonlinear correlation between the two variables.

B.

There is

insufficientinsufficient

evidence to support the claim of a linear correlation between the two variables.

C.

There is

sufficientsufficient

evidence to support the claim of a nonlinear correlation between the two variables.

D.

There is

sufficientsufficient

evidence to support the claim of a linear correlation between the two variables.

1. Identify the feature of the data that would be missed if part (b) was completed without constructing the scatterplot. Choose the correct answer below.

A.

The scatterplot reveals a distinct pattern that is not a straight-line pattern.

B.

The scatterplot reveals a distinct pattern that is a straight-line pattern with positive slope.

C.

The scatterplot reveals a distinct pattern that is a straight-line pattern with negative slope.

D.

The scatterplot does not reveal a distinct pattern.

Question is complete.

4

Listed below are annual data for various years. The data are weights (metric tons) of imported lemons and car crash fatality rates per 100,000 population. Construct a scatterplot, find the value of the linear correlation coefficient r, and find the P-value using

alphaαequals=0.050.05.

Is there sufficient evidence to conclude that there is a linear correlation between lemon imports and crash fatality rates? Do the results suggest that imported lemons cause car fatalities?

What are the null and alternative hypotheses?

A.

Upper H 0H0:

rhoρequals=0

Upper H 1H1:

rhoρless than<0

B.

Upper H 0H0:

rhoρequals=0

Upper H 1H1:

rhoρgreater than>0

C.

Upper H 0H0:

rhoρnot equals≠0

Upper H 1H1:

rhoρequals=0

D.

Upper H 0H0:

rhoρequals=0

Upper H 1H1:

rhoρnot equals≠0

Construct a scatterplot. Choose the correct graph below.

A.

020040060014151617xy

A scatterplot has a horizontal x-scale from 0 to 600 in increments of 100 and a vertical y-scale from 14 to 17 in increments of 0.5. Five points are plotted with coordinates as follows: (230, 15.9); (270, 15.7); (360, 15.4); (480, 15.2); (530, 14.9). All horizontal coordinates are approximate.

B.

020040060014151617xy

A scatterplot has a horizontal x-scale from 0 to 600 in increments of 100 and a vertical y-scale from 14 to 17 in increments of 0.5. Five points are plotted with coordinates as follows: (230, 14.9); (270, 15.2); (360, 15.4); (480, 15.7); (530, 15.9). All horizontal coordinates are approximate.

C.

020040060014151617xy

A scatterplot has a horizontal x-scale from 0 to 600 in increments of 100 and a vertical y-scale from 14 to 17 in increments of 0.5. Five points are plotted with coordinates as follows: (230, 15.9); (270, 15.7); (360, 15.4); (480, 15.7); (530, 15.9). All horizontal coordinates are approximate.

D.

020040060014151617xy

A scatterplot has a horizontal x-scale from 0 to 600 in increments of 100 and a vertical y-scale from 14 to 17 in increments of 0.5. Five points are plotted with coordinates as follows: (200, 14.9); (230, 15.9); (330, 16.2); (400, 15.1); (560, 15.3). All horizontal coordinates are approximate.

The linear correlation coefficient r is

(Round to three decimal places as needed.)

The test statistic t is

(Round to three decimal places as needed.)

The P-value is

(Round to three decimal places as needed.)

Because the P-value is

than the significance level

0.050.05,

there

sufficient evidence to support the claim that there is a linear correlation between lemon imports and crash fatality rates for a significance level of

alphaαequals=0.050.05.

Do the results suggest that imported lemons cause car fatalities?

A.

The results do not suggest any cause-effect relationship between the two variables.

B.

The results suggest that imported lemons cause car fatalities.

C.

The results suggest that an increase in imported lemons causes car fatality rates to remain the same.

D.

The results suggest that an increase in imported lemons causes in an increase in car fatality rates.

5

The data below shows the annual salaries (in millions) and the number of viewers (in millions) of eight television actors and actresses. Construct a scatterplot, find the value of the linear correlation coefficient r, and find the P-value using

alphaαequals=0.050.05.

Is there sufficient evidence to conclude that there is a linear correlation between the two variables?

What are the null and alternative hypotheses?

A.

Upper H 0H0:

rhoρnot equals≠0

Upper H 1H1:

rhoρequals=0

B.

Upper H 0H0:

rhoρequals=0

Upper H 1H1:

rhoρless than<0

C.

Upper H 0H0:

rhoρequals=0

Upper H 1H1:

rhoρgreater than>0

D.

Upper H 0H0:

rhoρequals=0

Upper H 1H1:

rhoρnot equals≠0

Construct a scatterplot. Choose the correct graph below.

A.

0204060801000510152025xy

A scatterplot has a horizontal scale labeled “x” from 0 to 100 in intervals of 20 and a vertical axis labeled “y” from 0 to 25 in intervals of 5. Eight points are plotted with approximate coordinates as follows: (14, 21); (30, 17); (34, 13); (50, 12); (68, 9); (70, 6); (84, 15); (86, 6).

B.

0204060801000510152025xy

A scatterplot has a horizontal scale labeled “x” from 0 to 100 in intervals of 20 and a vertical axis labeled “y” from 0 to 25 in intervals of 5. Eight points are plotted with approximate coordinates as follows: (2, 5); (6, 14); (10, 5); (10, 9); (12, 5); (14, 10); (34, 2); (98, 8).

C.

0204060801000510152025xy

A scatterplot has a horizontal scale labeled “x” from 0 to 100 in intervals of 20 and a vertical axis labeled “y” from 0 to 25 in intervals of 5. Eight points are plotted with approximate coordinates as follows: (12, 6); (26, 9); (28, 22); (42, 11); (48, 14); (62, 13); (68, 15); (88, 18).

D.

0204060801000510152025xy

A scatterplot has a horizontal scale labeled “x” from 0 to 100 in intervals of 20 and a vertical axis labeled “y” from 0 to 25 in intervals of 5. Eight points are plotted with approximate coordinates as follows: (12, 22); (24, 16); (34, 4); (38, 11); (54, 17); (68, 21); (73, 7); (86, 15).

The linear correlation coefficient r is

(Round to three decimal places as needed.)

The test statistic t is

(Round to three decimal places as needed.)

The P-value is

(Round to three decimal places as needed.)

Because the P-value is

than the significance level

0.050.05,

there

sufficient evidence to support the claim that there is a linear correlation between annual salaries (in millions) and the number of viewers (in millions) for a significance level of

alphaαequals=0.050.05.

Can the number of viewers be used to get a good sense of annual salaries?

A.

Knowing the number of viewers is helpful in getting a good sense for the annual salaries, because there does not appear to be a linear correlation between the two variables.

B.

Knowing the number of viewers is not helpful in getting a good sense for the annual salaries because there appears to be a linear correlation between the two variables.

C.

Knowing the number of viewers is not helpful in getting a good sense for the annual salaries because there does not appear to be a linear correlation between the two variables.

D.

Knowing the number of viewers is helpful in getting a good sense for the annual salaries because there appears to be a linear correlation between the two variables.

6

Which of the following is NOT true for a hypothesis test for correlation?

Choose the correct answer below.

A.

If

|r|less than or equals≤critical

value, we should fail to reject the null hypothesis and conclude that there is not sufficient evidence to support the claim of a linear correlation.

B.

If the P-value is greater than the significance level, we should fail to reject the null hypothesis and conclude that there is not sufficient evidence to support the claim of a linear correlation.

C.

If the P-value is less than or equal to the significance level, we should reject the null hypothesis and conclude that there is sufficient evidence to support the claim of a linear correlation.

D.

If

|r|greater than>critical

value, we should fail to reject the null hypothesis and conclude that there is not sufficient evidence to support the claim of a linear correlation.

7

A sample of

100100

women is obtained, and their heights (in inches) and pulse rates (in beats per minute) are measured. The linear correlation coefficient is

0.2110.211

and the equation of the regression line is

ModifyingAbove y with caret equals 17.9 plus 0.880 x<=”” path=””>y=17.9+0.880x,

where x represents height. The mean of the

100100

heights is

63.463.4

in and the mean of the

100100

pulse rates is

76.276.2

beats per minute. Find the best predicted pulse rate of a woman who is

6565

in tall. Use a significance level of

alpha equals 0.05α=0.05.

LOADING…

Click the icon to view the critical values of the Pearson correlation coefficient r.

The best predicted pulse rate of a woman who is

6565

in tall is

beats per minute.

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

8

se the given data to find the equation of the regression line. Examine the scatterplot and identify a characteristic of the data that is ignored by the regression line.

ModifyingAbove y with caret<=”” path=””>yequals=plus+x

(Round to two decimal places as needed.)

Create a scatterplot of the data. Choose the correct graph below.

A.

05101520250510152025xy

A scatterplot has a horizontal x-scale from 0 to 25 in intervals of 1 and a vertical y-scale from 0 to 25 in intervals of 1. Eleven points are plotted with approximate coordinates as follows: (5.5, 4); (8.5, 5); (11, 6); (13.5, 7); (15.5, 8); (17, 9); (18, 10); (19, 11); (19.5, 12); (19.5, 13); (19.5, 14).

B.

05101520250510152025xy

A scatterplot has a horizontal x-scale from 0 to 25 in intervals of 1 and a vertical y-scale from 0 to 25 in intervals of 1. Eleven points are plotted with approximate coordinates as follows: (4, 11); (5, 5.5); (6, 15.5); (7, 19); (8, 19.5); (9, 8.5); (10, 13.5); (11, 18); (12, 19.5); (13, 17); (14, 19.5).

C.

05101520250510152025xy

A scatterplot has a horizontal x-scale from 0 to 25 in intervals of 1 and a vertical y-scale from 0 to 25 in intervals of 1. Eleven points are plotted with approximate coordinates as follows: (4, 8); (5, 10); (6, 11); (7, 13); (8, 14); (9, 15); (10, 17); (11, 18); (12, 20); (13, 21); (14, 22).

D.

05101520250510152025xy

A scatterplot has a horizontal x-scale from 0 to 25 in intervals of 1 and a vertical y-scale from 0 to 25 in intervals of 1. Eleven points are plotted with approximate coordinates as follows: (4, 5.5); (5, 8.5); (6, 11); (7, 13.5); (8, 15.5); (9, 17); (10, 18); (11, 19); (12, 19.5); (13, 19.5); (14, 19.5).

Identify a characteristic of the data that is ignored by the regression line.

A.

There is no trend in the data.

B.

The data has a pattern that is not a staight line.

C.

There is an influential point that strongly affects the graph of the regression line.

D.

There is no characteristic of the data that is ignored by the regression line.

9

The data show systolic and diastolic blood pressure of certain people. Find the regression equation, letting the systolic reading be the independent (x) variable. Find the best predicted diastolic pressure for a person with a systolic reading of

Is the predicted value close to

66.466.4,

which was the actual diastolic reading? Use a significance level of 0.05.

LOADING…

Click the icon to view the critical values of the Pearson correlation coefficient r.

What is the regression equation?

ModifyingAbove y with caret<=”” path=””>yequals= 37.74−37.74plus+

(Round to two decimal places as needed.)

What is the best predicted diastolic pressure for a person with a systolic reading of

150150?

ModifyingAbove y with caret<=”” path=””>yequals=

(Round to one decimal place as needed.)

Is the predicted value close to

66.466.4,

which was the actual diastolic reading?

A.

The predicted value is very close to the actual diastolic reading.

B.

The predicted value is exactly the same as the actual diastolic reading.

C.

The predicted value is not close to the actual diastolic reading.

D.

The predicted value is close to the actual diastolic reading.

10

The data show the number of viewers for television stars with certain salaries. Find the regression equation, letting salary be the independent (x) variable. Find the best predicted number of viewers for a television star with a salary of

$33

million. Is the result close to the actual number of viewers,

4.04.0

million? Use a significance level of 0.05.

LOADING…

Click the icon to view the critical values of the Pearson correlation coefficient r.

What is the regression equation?

ModifyingAbove y with caret<=””

(Round to three decimal places as needed.)

What is the best predicted number of viewers for a television star with a salary of

$33

million?

million viewers (Round to one decimal place as needed.)

Is the result close to the actual number of viewers,

4.04.0

million?

A.

The result is not very close to the actual number of viewers of

4.04.0

million.

B.

The result is very close to the actual number of viewers of

4.04.0

million.

C.

The result is exactly the same as the actual number of viewers of

4.04.0

million.

D.

The result does not make sense given the context of the data.

11

When making predictions based on regression lines, which of the following is not listed as a consideration?

Choose the correct answer below.

A.

Use the regression equation for predictions only if the graph of the regression line on the scatterplot confirms that the regression line fits the points reasonably well.

B.

If the regression equation does not appear to be useful for making predictions, the best predicted value of a variable is its point estimate.

C.

Use the regression line for predictions only if the data go far beyond the scope of the available sample data.

D.

Use the regression equation for predictions only if the linear correlation coefficient r indicates that there is a linear correlation between the two variables.

12

Fill in the blank.

For a pair of sample x- and y-values, the ______________ is the difference between the observed sample value of y and the y-value that is predicted by using the regression equation.

For a pair of sample x- and y-values, the

is the difference between the observed sample value of y and the y-value that is predicted by using the regression equation.