statistics A company is evaluating the impact of a wellness program offered on-site
Chapter Problems 6
Answer the following. (3 pts
ea)
1. A
company is evaluating the impact of a wellness program offered on-site as a
means of reducing employee sick days. A
total of 8 employees agree to participate in the evaluation which lasts 12
weeks. Their sick days in the 12 months
prior to the start of the wellness program and again over the 12 months after
the completion of the program are recorded and are shown below. Is there a significant reduction in the
number of sick days taken after completing the wellness program? Use
the Sign Test at a 5% level of significance.
Complete the table below.
Employee
Sick
Days Taken in 12 Months Prior to Program
Sick
Days Taken in 12 Months Following program
Difference
(Reduction = Prior-After )
Sign
1
8
7
( )
( )
2
6
6
( )
( )
3
4
5
( )
( )
4
12
11
( )
( )
5
10
7
( )
( )
6
8
4
( )
( )
7
6
3
( )
( )
8
2
1
( )
( )
Alpha=________
n=________
Critical value=________
Smaller of the number of positive or negative
signs=________
Based on comparing the smaller of the number of
positive or negative signs to the Critical value which of the following is
(are) true?
A. There isstatistically significant
evidence at alpha=0.05 to show that the median difference (reduction) is
positive.
B. There is not statistically significant
evidence at alpha=0.05 to show that the median difference (reduction) is
positive.
C. There are not enough data points to reach a
conclusion.
D. The tied value makes the analysis suspect.
2.
A small study (n=10)
is designed to assess if there is an association between smoking in pregnancy
and low birth weight. Low birth weight
babies are those born less than 5.5 pounds.
The following data represent the birth weights, in pounds, of babies
born to mothers who reported smoking in pregnancy and those who did not.
Mother smoked in pregnancy 5.0 4.2 4.8 3.3 3.9
Mother did not smoke during pregnancy 5.1 4.9 5.3 5.4 4.6
Is there a significant difference in birth weights
between mother who smoked during pregnancy and those who did not? Apply the Mann Whitney U Test at a 5% level
of significance.
Complete the table below.
Total
Sample (Ordered Smallest to Largest)
Ranks
Mother
Smoked in Pregnancy
Mother
Did Not Smoke in Pregnancy
R
a
n
k
Smoked
Did
Not Smoke
Smoked
Did
Not Smoke
.0/msohtmlclip1/01/clip_image001.gif”>5.0
5.1
1
3.3
4.2
4.9
2
4.8
5.3
3
3.3
.0/msohtmlclip1/01/clip_image002.gif”>5.4
4
4.6
3.9
4.6
5
6
7
8
9
10
R1=____
R2=____
2. cont.
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Alpha=________
N1=________
N2=________
Critical value U=________
Smaller of U1 and U2 =________
Based on comparing the Smaller of U1
and U2 to the Critical value
which of the following is (are) true?
A. There issignificant evidence at alpha=0.05
to show that the populations of birth weights in mothers who smoked in
pregnancy and those who did not are not equal.
B. There is not significant evidence at alpha =0.05 to show
that the populations of birth weights in mothers who smoked in pregnancy
and those who did not are not equal.
C. There are not enough data points to reach a
conclusion.
D. The tied value makes the analysis suspect.
3.
The recommended daily
allowance of Vitamin A for children between 1 and 3 years of age is 400
micrograms (mcg). Vitamin A deficiency
is linked to a number of adverse health outcomes including poor eyesight,
susceptibility to infection, and dry skin.
The following are Vitamin A concentrations in children with and without
poor eyesight, a history of infection and dry skin.
With poor eyesight, a history 270 420 180 345 390 430
of infection and dry skin.
Free of poor eyesight, a history 450 500 395 380 430
of infection and dry skin.
Is there a
significant difference in Vitamin A concentrations between children with and without poor eyesight, a history of
infection and dry skin? Apply the
Mann Whitney U Test a 5% level of significance.
Complete the table below.
Total
Sample (Ordered Smallest to Largest)
Ranks
With
infection
Free
of infection
R
a
n
k
With
infection
Free
of infection
With
infection
Free
of infection
.0/msohtmlclip1/01/clip_image007.gif”>270
450
1
180
420
500
2
180
395
3
345
.0/msohtmlclip1/01/clip_image008.gif”>380
4
380
390
430
5
430
6
7
8
10
11
R1=____
R2=____
3. cont.
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.0/msohtmlclip1/01/clip_image012.gif”>
Alpha=________
N1=________
N2 =________
Critical value U=________
Smaller of U1 and U2 =________
Based on comparing the Smaller of U1
and U2 to the Critical value
which of the following is (are) true?
A. There isstatistically significant
evidence at α=0.05 to show thatthe populations of Vitamin A
concentrations in children with and without poor
eyesight, a history of infection and dry skinare not equal.
B. There is not statistically significant evidence at α=0.05
to show thatthe populations of Vitamin A concentrations in children with and without poor eyesight, a history of
infection and dry skinare not equal.
C. There are not enough data points to reach a
conclusion.
D. The tied value makes the analysis suspect.
4.
A study is conducted to assess the potential
benefits of an ayurvedic treatment to reduce high cholesterol. Seven patients agree to participate in the
study. Each has their cholesterol
measured at the start of the study and then again after 4 weeks taking a
popular herb called arjuna. Assess
whether there is there a difference in total cholesterol after taking the herb
using the Wilcoxon Signed Rank Test at a
5% level of significance.
Compete the tables below.
Participant
Total
Cholesterol
Before
Treatment
Total
Cholesterol
After
Treatment
Difference
(Before-After )
1
250
241
2
265
260
3
240
253
4
233
230
5
255
224
6
275
227
7
241
232
Ordered
Absolute Values of Differences
Ranks
Signed
Ranks
3
5
9
9
13
31
48
Total=>
28
W+ = 23 and W- = 5 (Recall that the sum of the ranks, ignoring the
signs, will always equal n(n+1)/2 = 7(8)/2.
The test statistic =________
Alpha=________
n=________
Critical value=________
Smaller of the number of positive or negative
signs________
4. cont.
Based on comparing the smaller of the number of
positive or negative signs to the Critical value which of the following is
(are) true?
A. There isstatistically significant evidence
at alpha=0.05 to show that the median difference is positive.
B. There is not statistically significant
evidence at alpha=0.05 to show that the median
difference is positive.
C. There are not enough data points to reach a
conclusion.
D. The tied value makes the analysis suspect.
5. An
investigator wants to test if there is a difference in endotoxin levels in
children who are exposed to endotoxin as a function of their proximity to
operating farms. The following are
endotoxin levels in units per milligram of dust sampled from children’s
mattresses, organized by children’s proximity to farms.
Within 5 Miles 54 62 78 90 70
5-24.9 Miles 28 42 39 81 65
25-49.9 Miles 37 29 30 50 53
50 Miles or More 36 19 22 28 27
Total
Sample (Ordered Smallest to Largest)
< 5 Miles 5-24.9 Miles 25-49.9 Miles 50+ Miles < 5 Miles 5-24.9 Miles 25-49.9 Miles 50+ Miles Apply theKruskal Wallis test at a 5% level of significance. Alpha=________ df= ________ Critical value=________ H=________ Based on comparing H to the critical value to the Critical value which of the following is (are) true? A. There issignificant evidence at alpha=0.05 t o show thatthe populations of endotoxin levels in children living varying distances from operating farms are not equal. B. There is not significant evidence at alpha =0.05 to show thatthe populations of endotoxin levels in children living varying distances from operating farms are not equal. C. There are not enough data points to reach a conclusion. D. The tied value makes the analysis suspect. Total Points for Chapter Problems 6: /15
