Question

In: Statistics and Probability

QUESTION 1 Which of the following is the Greek symbol chi? a. X b. ? c....

QUESTION 1

Which of the following is the Greek symbol chi?

a.

X
b.

?
c.

?
d.

?

1 points   

QUESTION 2

Researchers wanted to know whether it is better to give the diphtheria, tetanus and pertussis (DTaP) vaccine in the thigh or the arm, so they collected data on severe reactions to this vaccine in children aged 3 to 6 years old. What would be the best statistical test for them to utilize?

a.

One-sample chi-square
b.

Linear regression
c.

T-test
d.

Two-sample chi-square

1 points   

QUESTION 3

If you have 30 respondents identifying their political preference (i.e., Democrat, Republican, Independent), what would be the expected frequency for each category?

a.

10
b.

30
c.

40
d.

20

1 points   

QUESTION 4

You use the CHISQ.TEST function in Excel, and receive a value of 0.9864. This value represents the _______.

a.

degrees of freedom
b.

p value
c.

chi-square statistic
d.

obtained value

1 points   

QUESTION 5

One assumption of the chi-square statistic is that each observation in a set of data is ______.

a.

dependent on all other observations
b.

interrelated to other observations
c.

independent of all other observations
d.

independent of some observations and dependent on others

1 points   

QUESTION 6

Use the following information for problems 6-8.

X 2(5) = 3.75, p < 0.05

How many categories were in this study?

a.

6
b.

0.05
c.

3.75
d.

5

1 points   

QUESTION 7

What is the X 2value?

a.

3.75
b.

5
c.

6
d.

0.05

1 points   

QUESTION 8

True or False, this finding is statistically significant.

True

False

1 points   

QUESTION 9

One study of Medical College Admissions Test (MCAT) compared the ethnicity of test takers with the overall student population, in order to see if the ethnicity of test takers was representative of the overall population. This information is presented in the following table. Conduct a chi-square test at the ? = 0.05 level.

Use the results of this analysis to answer problems 9-13

Ethnicity

Overall student

percentage

# of students

observed

# of students

expected

Asian, Asian American or Pacific Islander

5.4%

113

Black or African American

14.5%

98

Hispanic or Latino

15.9%

141

American Indian or Alaska Native

1.2%

25

White

61.6%

604

Not reported/other

1.4%

45

Totals

100%

1026

What is the degrees of freedom for this test?

a.

2
b.

5
c.

6
d.

1

1 points   

QUESTION 10

What is the expected value for the number of students who were Hispanic or Latino?

a.

163.13
b.

159
c.

141.5
d.

171

1 points   

QUESTION 11

What is the chi-square value?

a.

5.35
b.

37.89
c.

1370.02
d.

159.92

1 points   

QUESTION 12

What is the critical value?

a.

15.08
b.

12.59
c.

11.07         
d.

3.75

1 points   

QUESTION 13

True or False, this finding is statistically significant.

True

False

1 points   

QUESTION 14

A manager of a sports club believes that there is a relationship between the age of a member and choice of sport. The sports club collects information on members and their choice of sport. This information is presented in the following table. Conduct a two-sample chi-square test to test the belief that the age of a member is related to the choice of sport. Use an ? of 0.05.

Use the results of this analysis to answer problems 14-20

Racquetball

Tennis

Swimming

18-25

42

58

72

26-30

58

76

60

31-40

30

38

65

41-60

46

65

33

60 and over

53

41

58

What is the null hypothesis?

a.

There is no difference between the groups
b.

The groups are not equal
c.

Age and sport choice are independent
d.

H0 = P1 = P2 = P3 = P4 = P5

1 points   

QUESTION 15

What is the formula to determine the degrees of freedom for this test?

a.

k -1
b.

c-1
c.

(r – 1) (c – 1)
d.

r-1

1 points   

QUESTION 16

What is the chi-square statistic?  

a.

31.2
b.

8
c.

27.35
d.

3.90

1 points   

QUESTION 17

What is the expected value for 31 – 40 year olds who play tennis?

a.

46.51
b.

278
c.

38
d.

48.18

1 points   

QUESTION 18

True or False, this finding is statistically significant.

True

False

1 points   

QUESTION 19

Based on this information, the researcher should make the decision to ___________.

a.

reject the null hypothesis
b.

fail to reject the null hypothesis

1 points   

QUESTION 20

How do you interpret this finding? There ____ enough evidence to conclude that there is a difference in sport preference based on age group at the 0.05 significance level.

a.

is
b.

is not

Solutions

Expert Solution

Result:

QUESTION 1

Which of the following is the Greek symbol chi?

?

a.

X

b.

?

c.

?

d.

?

1 points   

QUESTION 2

Researchers wanted to know whether it is better to give the diphtheria, tetanus and pertussis (DTaP) vaccine in the thigh or the arm, so they collected data on severe reactions to this vaccine in children aged 3 to 6 years old. What would be the best statistical test for them to utilize?

a.

One-sample chi-square

b.

Linear regression

c.

T-test

Answer: d.

Two-sample chi-square

1 points   

QUESTION 3

If you have 30 respondents identifying their political preference (i.e., Democrat, Republican, Independent), what would be the expected frequency for each category?

Answer: a.

10

b.

30

c.

40

d.

20

1 points   

QUESTION 4

You use the CHISQ.TEST function in Excel, and receive a value of 0.9864. This value represents the _______.

a.

degrees of freedom

b.

p value

Answer: c.

chi-square statistic

d.

obtained value

1 points   

QUESTION 5

One assumption of the chi-square statistic is that each observation in a set of data is ______.

a.

dependent on all other observations

b.

interrelated to other observations

Answer: c.

independent of all other observations

d.

independent of some observations and dependent on others

1 points   

QUESTION 6

Use the following information for problems 6-8.

X 2(5) = 3.75, p < 0.05

How many categories were in this study?

Answer: a.

6

b.

0.05

c.

3.75

d.

5

1 points   

QUESTION 7

What is the X 2value?

Answer: a.

3.75

b.

5

c.

6

d.

0.05

1 points   

QUESTION 8

True or False, this finding is statistically significant.

True

Answer: False

1 points   

QUESTION 9

One study of Medical College Admissions Test (MCAT) compared the ethnicity of test takers with the overall student population, in order to see if the ethnicity of test takers was representative of the overall population. This information is presented in the following table. Conduct a chi-square test at the ? = 0.05 level.

Use the results of this analysis to answer problems 9-13

Ethnicity

Overall student

percentage

# of students

observed

# of students

expected

Asian, Asian American or Pacific Islander

5.4%

113

Black or African American

14.5%

98

Hispanic or Latino

15.9%

141

American Indian or Alaska Native

1.2%

25

White

61.6%

604

Not reported/other

1.4%

45

Totals

100%

1026

What is the degrees of freedom for this test?

a.

2

Answer: b.

5

c.

6

d.

1

1 points   

Goodness of Fit Test

observed

expected

O - E

(O - E)² / E

113

55.404

57.596

59.875

98

148.770

-50.770

17.326

141

163.134

-22.134

3.003

25

12.312

12.688

13.075

604

632.016

-28.016

1.242

45

14.364

30.636

65.341

Total

1026

1026.000

0.000

159.863

159.86

chi-square

5

df

0.0000

p-value

QUESTION 10

What is the expected value for the number of students who were Hispanic or Latino?

Answer: a.

163.13

b.

159

c.

141.5

d.

171

1 points   

QUESTION 11

What is the chi-square value?

a.

5.35

b.

37.89

c.

1370.02

Answer: d.

159.92

1 points   

QUESTION 12

What is the critical value?

a.

15.08

b.

12.59

Answer: c.

11.07         

d.

3.75

1 points   

QUESTION 13

True or False, this finding is statistically significant.

Answer: True

False

1 points   

QUESTION 14

A manager of a sports club believes that there is a relationship between the age of a member and choice of sport. The sports club collects information on members and their choice of sport. This information is presented in the following table. Conduct a two-sample chi-square test to test the belief that the age of a member is related to the choice of sport. Use an ? of 0.05.

Use the results of this analysis to answer problems 14-20

Racquetball

Tennis

Swimming

18-25

42

58

72

26-30

58

76

60

31-40

30

38

65

41-60

46

65

33

60 and over

53

41

58

What is the null hypothesis?

a.

There is no difference between the groups

b.

The groups are not equal

Answer: c.

Age and sport choice are independent

d.

H0 = P1 = P2 = P3 = P4 = P5

1 points   

QUESTION 15

What is the formula to determine the degrees of freedom for this test?

a.

k -1

b.

c-1

Answer: c.

(r – 1) (c – 1)

d.

r-1

1 points   

Observed Frequencies

Column variable

Calculations

Racquetball

Tennis

Swimming

Total

fo-fe

18-25

42

58

72

172

-7.5447

-2.1459

9.6906

26-30

58

76

60

194

2.1182

8.1610

-10.2792

31-40

30

38

65

133

-8.3107

-8.5082

16.8189

41-60

46

65

33

144

4.5208

14.6453

-19.1660

60 and over

53

41

58

152

9.2164

-12.1522

2.9358

Total

229

278

288

795

Expected Frequencies

Column variable

Racquetball

Tennis

Swimming

Total

(fo-fe)^2/fe

18-25

49.5447

60.1459

62.3094

172

1.1489

0.0766

1.5071

26-30

55.8818

67.8390

70.2792

194

0.0803

0.9818

1.5035

31-40

38.3107

46.5082

48.1811

133

1.8028

1.5565

5.8711

41-60

41.4792

50.3547

52.1660

144

0.4927

4.2595

7.0417

60 and over

43.7836

53.1522

55.0642

152

1.9400

2.7784

0.1565

Total

229

278

288

795

Data

Level of Significance

0.05

Number of Rows

5

Number of Columns

3

Degrees of Freedom

8

Results

Critical Value

15.5073

Chi-Square Test Statistic

31.1972

p-Value

0.0001

Reject the null hypothesis

QUESTION 16

What is the chi-square statistic?  

Answer: a.

31.2

b.

8

c.

27.35

d.

3.90

1 points   

QUESTION 17

What is the expected value for 31 – 40 year olds who play tennis?

Answer: a.

46.51

b.

278

c.

38

d.

48.18

1 points   

QUESTION 18

True or False, this finding is statistically significant.

Answer: True

False

1 points   

QUESTION 19

Based on this information, the researcher should make the decision to ___________.

Answer: a.

reject the null hypothesis

b.

fail to reject the null hypothesis

1 points   

QUESTION 20

How do you interpret this finding? There ____ enough evidence to conclude that there is a difference in sport preference based on age group at the 0.05 significance level.

Answer: a.

is

b.

is not

orchestra answered 1 year ago
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