Question 1

A sample of eight people attended a two day course that prepares students for college admission testing. The students were given a pretest before the course and a posttest after the course. The results were as follows.
$\begin{array} { l | c c c c c c c c } 
\text { Student } & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \
\hline \text { Pretest } & 66 & 74 & 74 & 71 & 70 & 72 & 65 & 66 \
\text { Posttest } & 79 & 76 & 63 & 67 & 64 & 89 & 78 & 74
\end{array}$

a) Compute the test statistic 
b) Can you conclude that the median scores differ between the pretest and posttest? Use the α = 0.10
Level of significance.

Accepted Answer

A)  a) S=10
b) We cannot conclude that the median of the pretests and posttests are different. 
B)  a) S=10
b) We can conclude that the median of the pretests and posttests are different. 
C)  a) S=9
b) We cannot conclude that the median of the pretests and posttests are different. 
D)  a) S=9
b) We can conclude that the median of the pretests and posttests are different.

Question 2

Find the critical value at the $\alpha = 0.05$ = 0.05 level for the following sample, for testing H0:m=55 versus  H1:m>55.
40 70 63 55 44 69 67 54 55 70 66 53 67 64

Accepted Answer

A) 4 
B) 2 
C) 1 
D) 3

Question 3

Given $n _ { 1 } = 14 , n _ { 2 } = 26 , \mathrm {~S} = 283 , \text { and } H _ { 1 } : \mu _ { 1 } < \mu _ { 2 } \text {, }$ compute $\mu _ { s }$

Accepted Answer

A)  287 
B)  -0.11 
C)  35.27 
D)  316

Question 4

Fill in the blank with the appropriate word or phrase. The null hypothesis for the rank-sum test is that the two population $?$ are equal.

Accepted Answer

A)  modes 
B)  rank-sums 
C)  medians 
D)  means

Question 5

For the following data, compute the test statistic and the critical value, and determine whether to reject $H _ { 0 }$ at the $\alpha = 0.10$ level.
$\begin{array} { l | l | l | l | l | l | l | l | l } 
\text { Sample A } & 40 & 51 & 51 & 45 & 42 & 44 & 43 & 53 \
\hline \text { Sample B } & 25 & 40 & 34 & 51 & 29 & 29 & 38 & 62
\end{array}$

Accepted Answer

A)  S=5, Critical value is 6, Reject H0 
B)  S=5, Critical value is 6, Do not reject H0 
C)  S=6, Critical value is 4, Reject H0 
D)  S=6, Critical value is 4, Do not reject H0

Question 6

If the test value for a signed-rank test is 18, the sample size is 13, and the test is to be carried out at the $\alpha = 0.05$ level of significance, should the null hypothesis be rejected? Use the table of critical
Values for the signed-rank test below. 
$\begin{array} { c | c c c c } 
\boldsymbol { n } & \alpha = 0.10 & \alpha = 0.05 & \alpha = 0.02 & \alpha = 0.01 \
\hline 9 & 8 & 6 & 3 & 2 \
10 & 11 & 8 & 5 & 3 \
11 & 14 & 11 & 7 & 5 \
12 & 17 & 14 & 10 & 7 \
13 & 21 & 17 & 13 & 10
\end{array}$

Accepted Answer

A)  Reject H0  because the test value 18 is less than the critical value 20 . 
B)  Do not reject  H0  because the test value 18 is less than the critical value 20 . 
C)  Reject  H0 because the test value 18 is greater than the critical value 17 . 
D)  Do not reject  H0 because the test value 18 is greater than the critical value 17 .

Question 7

The following data was collected as part of a study examining whether there is a difference between the number of hours men and women watch television. The values represent the number of hours a Subject watched television on a designated Tuesday night. Lower values rank ahead of higher ones. $$\begin{array} { l | l l l l l l l l l l l l } 
\text { Men } & 2.0 & 1.5 & 3.0 & 2.5 & 2.0 & 1.0 & 0.0 & 2.0 & 1.5 & 2.5 & 2.0 & 2.0 \
\hline \text { Women } & 2.0 & 2.5 & 1.0 & 1.0 & 1.5 & 2.5 & 2.0 & 1.0 & 2.0 & 1.5 & 1.0 & 0.0
\end{array}$$ 
a) Calculate the P-value.
b) Can you conclude that the median times watching television are different? Use the $\alpha = 0.10$ level Of significance.

Accepted Answer

A) 
a) 0.1251
b) Yes, you can not conclude that the median times are different. 
B) 
a) 0.1251.
b) No, you can not conclude that the median times are different. 
C) 
a) 0.2502.
b) No, you can not conclude that the median times are different. 
D) 
a) 0.2502
b) Yes, you can not conclude that the median times are different.

Exam 15: Nonparametric Statistics

Find the critical value at the $\alpha = 0.05$ = 0.05 level for the following sample, for testing H₀:m=55 versus H₁:m>55. 40 70 63 55 44 69 67 54 55 70 66 53 67 64

Given $n _ { 1 } = 14 , n _ { 2 } = 26 , \mathrm {~S} = 283 , \text { and } H _ { 1 } : \mu _ { 1 } < \mu _ { 2 } \text {, }$ compute $\mu _ { s }$

Fill in the blank with the appropriate word or phrase. The null hypothesis for the rank-sum test is that the two population $?$ are equal.

Exam 15: Nonparametric Statistics

Find the critical value at the α=0.05\alpha = 0.05α=0.05 = 0.05 level for the following sample, for testing H0:m=55 versus H1:m>55. 40 70 63 55 44 69 67 54 55 70 66 53 67 64

Given n1=14,n2=26, S=283, and H1:μ1<μ2, n _ { 1 } = 14 , n _ { 2 } = 26 , \mathrm {~S} = 283 , \text { and } H _ { 1 } : \mu _ { 1 } < \mu _ { 2 } \text {, }n1​=14,n2​=26, S=283, and H1​:μ1​<μ2​, compute μs\mu _ { s }μs​

Fill in the blank with the appropriate word or phrase. The null hypothesis for the rank-sum test is that the two population ??? are equal.

Find the critical value at the $\alpha = 0.05$ = 0.05 level for the following sample, for testing H₀:m=55 versus H₁:m>55. 40 70 63 55 44 69 67 54 55 70 66 53 67 64

Given $n _ { 1 } = 14 , n _ { 2 } = 26 , \mathrm {~S} = 283 , \text { and } H _ { 1 } : \mu _ { 1 } < \mu _ { 2 } \text {, }$ compute $\mu _ { s }$

Fill in the blank with the appropriate word or phrase. The null hypothesis for the rank-sum test is that the two population $?$ are equal.