In: Statistics and Probability
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 |
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 |
|