9.3

1)Listed below are body temperatures from five different subjects measured at 8 AM and again at 12 AM. Find the values of d and sd. Ingeneral, what does d represent?

Temperature(F)at8AM

98.3

99.2

97.1

97.7

97.6

Temperature(F)at12AM

98.8

99.7

97.6

97.4

97.9

Let the temperature at 8 AM be the firstsample, and the temperature at 12 AM be the second sample. Find the values of d and sd.

2)The following data lists the ages of a random selection of actresses when they won an award in the category of BestActress, along with the ages of actors when they won in the category of Best Actor. The ages are matched according to the year that the awards were presented. Complete parts(a) and(b) below.

Actress(years)

28

28

28

27

37

28

25

45

28

32

Actor(years)

56

33

40

40

30

31

46

35

36

39

a. Use the sample data with a 0.01 significance level to test the claim that for the population of ages of Best Actresses and BestActors, the differences have a mean less than 0(indicating that the Best Actresses are generally younger than BestActors).

In thisexample, d is the mean value of the differences d for the population of all pairs ofdata, where each individual difference d is defined as theactress's age minus theactor's age. What are the null and alternative hypotheses for the hypothesistest?

H0: d

greater than

>

equals

=

not equals

less than

<

nothing

year(s)

H1: d

equals

=

not equals

less than

<

greater than

>

nothing

year(s)

(Type integers or decimals. Do notround.)

Enter your answer in the edit fields and then click Check Answer

3)The following data lists the ages of a random selection of actresses when they won an award in the category of BestActress, along with the ages of actors when they won in the category of Best Actor. The ages are matched according to the year that the awards were presented. Complete parts(a) and(b) below.

Actress(years)

28

28

28

27

37

28

25

45

28

32

Actor(years)

56

33

40

40

30

31

46

35

36

39

a. Use the sample data with a 0.01 significance level to test the claim that for the population of ages of Best Actresses and BestActors, the differences have a mean less than 0(indicating that the Best Actresses are generally younger than BestActors).

In thisexample, d is the mean value of the differences d for the population of all pairs ofdata, where each individual difference d is defined as theactress's age minus theactor's age. What are the null and alternative hypotheses for the hypothesistest?

H0: d

greater than

>

equals

=

not equals

less than

<

nothing

year(s)

H1: d

equals

=

not equals

less than

<

greater than

>

nothing

year(s)

(Type integers or decimals. Do notround.)

Enter your answer in the edit fields and then click Check Answer

4)The following data lists the ages of a random selection of actresses when they won an award in the category of BestActress, along with the ages of actors when they won in the category of Best Actor. The ages are matched according to the year that the awards were presented. Complete parts(a) and(b) below.

Actress(years)

28

28

28

27

37

28

25

45

28

32

Actor(years)

56

33

40

40

30

31

46

35

36

39

a. Use the sample data with a 0.01 significance level to test the claim that for the population of ages of Best Actresses and BestActors, the differences have a mean less than 0(indicating that the Best Actresses are generally younger than BestActors).

In thisexample, d is the mean value of the differences d for the population of all pairs ofdata, where each individual difference d is defined as theactress's age minus theactor's age. What are the null and alternative hypotheses for the hypothesistest?

H0: d

greater than

>

equals

=

not equals

less than

<

nothing

year(s)

H1: d

equals

=

not equals

less than

<

greater than

>

nothing

year(s)

(Type integers or decimals. Do notround.)

Enter your answer in the edit fields and then click Check Answer

5)The accompanying table lists the numbers of words spoken in a day by each member of 56 different randomly selected couples. Complete parts(a) and(b) below.

LOADING...

Click the icon to view the data on words spoken in a day by the couples.

a. Use a 0.05 significance level to test the claim that amongcouples, males speak fewer words in a day than females.

In thisexample, d is the mean value of the differences d for the population of all pairs ofdata, where each individual difference d is defined as the words spoken by the male minus words spoken by the female. What are the null and alternative hypotheses for the hypothesistest?

H0: d

less than

<

greater than

>

not equals

equals

=

nothing

word(s)

H1: d

greater than

>

equals

=

not equals

less than

<

nothing

word(s)

(Type integers or decimals. Do notround.)

Enter your answer in the edit fields and then click Check Answer.

9.4

1)nswer the following questions on the F test statistic. Complete parts(a) through(d) below.

a. If s21 represents the larger of two samplevariances, can the F test statistic ever be less than1?

A.

No, because the ratio s21s22 will always be greater than 1.

B.

Yes, because the ratio s22s21 will always be less than 1.

C.

No, because the ratio s22s21 will always be greater than 1.

D.

Yes, because the ratio s21s22 will always be less than 1.

2)Researchers measured skulls from different time periods in an attempt to determine whether interbreeding of cultures occurred. Results are given below. Assume that both samples are independent simple random samples from populations having normal distributions. Use a 0.05 significance level to test the claim that the variation of maximal skull breadths in 4000 B.C. is the same as the variation in A.D. 150.

n

x

s

4000 B.C.

30

131.06 mm

5.11 mm

A.D. 150

30

136.73 mm

5.33 mm

What are the null and alternativehypotheses?

A.

H0: 21=22

H1: 21<22

B.

H0: 21=22

H1: 2122

C.

H0: 2122

H1: 21=22

D.

H0: 21=22

H1: 2122

Click to select your answer and then click Check Answer.

3)TQuestion Help

Researchers conducted an experiment to test the effects of alcohol. Errors were recorded in a test of visual and motor skills for a treatment group of 21 people who drank ethanol and another group of 21 people given a placebo. The errors for the treatment group have a standard deviation of 2.20, and the errors for the placebo group have a standard deviation of 0.83. Use a 0.05 significance level to test the claim that the treatment group has errors that vary significantly more than the errors of the placebo group. Assume that the two populations are normally distributed.

What are the null and alternativehypotheses?

A.

H0: 21=22

H1: 2122

B.

H0: 21=22

H1: 21>22

C.

H0: 2122

H1: 21=22

D.

H0: 21=22

H1: 21<

4)

The accompanying table gives results from a study of words spoken in a day by men and women. Assume that both samples are independent simple random samples from populations having normal distributions. Use a 0.05 significance level to test the claim that the numbers of words spoken in a day by men vary more than the numbers of words spoken in a day by women.

n

x

s

Men

185

15,667.4

8,632.6

Women

210

16,215.2

7,301.4

What are the null and alternativehypotheses?

A.

H0: 21=22

H1: 21>22

B.

H0: 21=22

H1: 2122

C.

H0: 21=22

H1: 21<22

D.

H0: 2122

H1: 21=

5)A study was conducted to determine whether magnets were effective in treating pain. The values represent measurements of pain using the visual analog scale. Assume that both samples are independent simple random samples from populations having normal distributions. Use a 0.05 significance level to test the claim that those given a sham treatment have pain reductions that vary more than the pain reductions for those treated with magnets.

n

x

s

Sham

20

0.43

1.58

Magnet

20

0.47

0.93

What are the null and alternativehypotheses?

A.

H0: 21=22

H1: 21<22

B.

H0: 21=22

H1: 2122

C.

H0: 21=22

H1: 21>22

D.

H0: 2122

H1: 21=22

Click to select your answer and then click Check Answer.

10.1

1)

Twenty different statistics students are randomly selected. For each ofthem, their body temperature (C) is measured and their head circumference(cm) is measured.

a. For this sample of paireddata, what does rrepresent, and what does represent?

b. Without doing any research orcalculations, estimate the value of r.

c. Does r change if body temperatures are converted to Fahrenheitdegrees?

a. Choose the correct answer below.

A.

r is a statistic that represents the proportion of the variation in head circumference that can be explained by variation in bodytemperature, and is a parameter that represents the value of the linear correlation coefficient that would be computed by using all of the paired data in the population of all statistics students.

B.

r is a statistic that represents the value of the linear correlation coefficient computed from the paired sampledata, and is a parameter that represents the proportion of the variation in head circumference that can be explained by variation in body temperature.

C.

r is a statistic that represents the value of the linear correlation coefficient computed from the paired sampledata, and is a parameter that represents the value of the linear correlation coefficient that would be computed by using all of the paired data in the population of all statistics students.

D.

r is a parameter that represents the value of the linear correlation coefficient that would be computed by using all of the paired data in the population of all statisticsstudents, and is a statistic that represents the value of the linear correlation coefficient computed from the paired sample data.

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

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.

3)

Match these values of r with the accompanyingscatterplots: 1, 0.995, 0.437, 1, and 0.79.

LOADING...

Click the icon to view the scatterplots.

Match the values of r to the scatterplots.

Scatterplot1, r=

negative 1

1

0.79

0.79

1

1

0.995

0.995

negative 0.437

0.437

Scatterplot2, r=

negative 0.437

0.437

negative 1

1

0.995

0.995

0.79

0.79

1

1

Scatterplot3, r=

1

1

0.79

0.79

negative 0.437

0.437

negative 1

1

0.995

0.995

Scatterplot4, r=

0.79

0.79

0.995

0.995

1

1

negative 0.437

0.437

negative 1

1

Scatterplot5, r=

negative 1

1

0.995

0.995

negative 0.437

0.437

1

1

0.79

0.79

Click to select your answer(s) and then click Check Answer.

4)Fifty-four wild bears wereanesthetized, and then their weights and chest sizes were measured and listed in a data set. Results are shown in the accompanying display. Is there sufficient evidence to support the claim that there is a linear correlation between the weights of bears and their chestsizes? When measuring an anesthetizedbear, is it easier to measure chest size thanweight? Ifso, does it appear that a measured chest size can be used to predict theweight? Use a significance level of =0.05.

Correlation Results

Correlationcoeff, r:

0.956094

Criticalr:

0.2680855

P-value (twotailed):

0.000

Determine the null and alternative hypotheses.

H0:

greater than

>

less than

<

equals

=

not equals

nothing

H1:

greater than

>

less than

<

equals

=

not equals

nothing

(Type integers or decimals. Do notround.)

Enter your answer in the edit fields and then click Check Answer.

5)Use the given data set to complete parts(a) through(c) below.(Use =0.05.)

x

10

8

13

9

11

14

6

4

12

7

5

y

9.15

8.15

8.74

8.77

9.25

8.09

6.14

3.09

9.14

7.26

4.74

LOADING...

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

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

A.

0

4

8

12

16

0

2

4

6

8

10

x

y

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 strictly follow the pattern of a curve that rises from left to right passing through the points (4, 3) and (7, 7.2) to a peak at (11, 9.2) and then falls to (14, 8). All coordinates are approximate.

B.

0

4

8

12

16

0

2

4

6

8

10

x

y

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 strictly follow the pattern of a curve that rises from left to right passing through the point is (4, 1), (8, 2.4), and (14, 8). All coordinates are approximate.

C.

0

4

8

12

16

0

2

4

6

8

10

x

y

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 strictly follow the pattern of a line passing through the points (4, 2) and (14, 7). All coordinates are approximate.

D.

0

4

8

12

16

0

2

4

6

8

10

x

y

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 strictly follow the pattern of a line passing through the points (4, 6) and (14, 1). All coordinates are approximate.

Click to select your answer and then click Check Answer.

6)Use the given data set to complete parts(a) through(c) below.(Use =0.05.)

x

10

8

13

9

11

14

6

4

12

7

5

y

7.46

6.77

12.74

7.11

7.81

8.85

6.08

5.39

8.14

6.43

5.73

LOADING...

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

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

A.

0

4

8

12

16

0

4

8

12

16

x

y

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 plotted points strictly follow the pattern of a line that passes through the points (4, 6) and (14, 1). All coordinates are approximate.

B.

0

4

8

12

16

0

4

8

12

16

x

y

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 plotted points strictly follow the pattern of a curve passing through the points (4, 1), (8, 2.4), and (14, 8). All coordinates are approximate.

C.

0

4

8

12

16

0

4

8

12

16

x

y

A scatterplot has a horizontal x-scale from 0 to 16 in increments of 2 and a vertical y-scale from 0 to 16 in increments of 2. Eleven points are plotted. Ten of the plotted points strictly follow the pattern of a line rising from left to right passing through the points (4, 5.4) and (14, 8.8). A point is plotted at (13, 12.8). All coordinates are approximate.

D.

0

4

8

12

16

0

4

8

12

16

x

y

7)

Police sometimes measure shoe prints at crime scenes so that they can learn something about criminals. Listed below are shoe printlengths, footlengths, and heights of males. Construct ascatterplot, find the value of the linear correlation coefficientr, and find theP-value of r. Determine whether there is sufficient evidence to support a claim of linear correlation between the two variables. Based on theseresults, does it appear that police can use a shoe print length to estimate the height of amale? Use a significance level of =0.01.

Shoe Print(cm)

28.8

28.8

32.7

33.0

27.0

Foot Length(cm)

26.3

25.8

28.3

27.0

25.9

Height(cm)

170.1

183.9

178.5

173.3

172

Construct a scatterplot. Choose the correct graph below.

A.

25

35

160

200

ShoePrint(cm)

Height(cm)

A scatterplot has a horizontal axis labeled Shoe Print in centimeters from 25 to 35 in increments of 1 and a vertical axis labeled Height in centimeters from 160 to 200 in increments of 5. Five points are plotted with coordinates as follows: (27.0, 172) (28.8, 170.1); (28.8, 183.9); (32.7, 178.5); (33.0, 173.3).

B.

25

35

160

200

ShoePrint(cm)

Height(cm)

A scatterplot has a horizontal axis labeled Shoe Print in centimeters from 25 to 35 in increments of 1 and a vertical axis labeled Height in centimeters from 160 to 200 in increments of 5. Five points are plotted with coordinates as follows: (27, 173.3); (27.3, 178.5); (31.2, 183.9); (31.2, 170.1); (33, 172).

C.

25

35

160

200

ShoePrint(cm)

Height(cm)

A scatterplot has a horizontal axis labeled Shoe Print in centimeters from 25 to 35 in increments of 1 and a vertical axis labeled Height in centimeters from 160 to 200 in increments of 5. Five points are plotted with coordinates as follows: (27, 186.7); (27.3, 181.5); (31.2, 176.1); (31.2, 189.9); (33, 188).

D.

25

35

160

200

ShoePrint(cm)

Height(cm)

8)Listed below are the overhead widths(in cm) of seals measured from photographs and the weights(in kg) of the seals. Construct ascatterplot, find the value of the linear correlation coefficientr, and find the critical values of r using =0.05. Is there sufficient evidence to conclude that there is a linear correlation between overhead widths of seals from photographs and the weights of theseals?

Overhead Width

7.1

7.6

9.6

9.3

8.6

8.3

Weight

112

174

238

201

196

192

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

Construct a scatterplot. Choose the correct graph below.

A.

7

10

100

300

width(cm)

weight(kg)

A scatterplot has a horizontal scale labeled "width in centimeters" from 7 to 10 in increments of 0.5 and a vertical scale labeled "weight in kilograms" from 100 to 300 in increments of 20. Six plotted points follow the pattern of a line rising from left to right passing throught points (7.4, 160) and (9.9, 290).

B.

7

10

100

300

width(cm)

weight(kg)

A scatterplot has a horizontal scale labeled "width in centimeters" from 7 to 10 in increments of 0.5 and a vertical scale labeled "weight in kilograms" from 100 to 300 in increments of 20. Six plotted points follow the pattern of a line rising from left to right passing through the points (7.1, 110) and (9.6, 240).

C.

7

10

100

300

width(cm)

weight(kg)

A scatterplot has a horizontal scale labeled "width in centimeters" from 7 to 10 in increments of 0.5 and a vertical scale labeled "weight in kilograms" from 100 to 300 in increments of 20. Six plotted points follow the pattern of a line falling from left to right passing through the points (7.4, 240) and (9.9, 110).

D.

7

10

100

300

width(cm)

weight(kg)

A scatterplot has a horizontal scale labeled "width in centimeters" from 7 to 10 in increments of 0.5 and a vertical scale labeled "weight in kilograms" from 100 to 300 in increments of 20. Six plotted points follow the pattern of a line falling from left to right passing through the points (7.1, 290) and (9.6, 160).