A study was conducted to assess whether there is a difference in two analgesic drugs (drug A and B) in atients suffering from arthritis. Each of the 18 patients involved are given both of the drugs at an interval the effects of the earlier drug to clear before administering the second drug and the time it takes for the recorded. A nonparametric approach is adopted as there were no reasonable grounds to assume normality. le is provided as part of the analysis.
A study was conducted to assess whether there is a difference in two analgesic drugs (drug A and B) in atients suffering from arthritis. Each of the 18 patients involved are given both of the drugs at an interval the effects of the earlier drug to clear before administering the second drug and the time it takes for the recorded. A nonparametric approach is adopted as there were no reasonable grounds to assume normality. le is provided as part of the analysis.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
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Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
Question
![[Questions 35-37] A study was conducted to assess whether there is a difference in two analgesic drugs (drug A and B) in
relieving pain in patients suffering from arthritis. Each of the 18 patients involved are given both of the drugs at an interval
sufficient to allow the effects of the earlier drug to clear before administering the second drug and the time it takes for the
pain to go away is recorded. A nonparametric approach is adopted as there were no reasonable grounds to assume normality.
The following table is provided as part of the analysis.
d -diff +diff | f. total f Ranks
Ave ranks
0.1
-0.1
1
1
1
0.2
-0.2
1
2
2
0.3
0.3
1
3
3
0.6
-0.6
1
4
0.7
-0.7
1
1
5
1.1
1.1
1
1
6
1.3
-1.3
1
7
1.5
1.5
2
2
8-9
8.5
1.8
1
1.8
2
3
10-12
10
11
12
13.5
15
16
2
2
1
1
13
2.1
2.1
1
1
14
2.3
2.3
15-16
2.6
2.6
17
12.4
12.4
1
1
18
35. Which is the correct set of hypotheses for this study?
(a) Ho : A4 = An vs Hị : AA# Ag.
(b) Ho : A = 0 vs H : A # 0.
(c) Hị : H4 vs Hị :44 = 0.
(d) Ho : HA = HB Vs H1 : µA HB-
36. What is the numerical value of R1, the rank sum for d, > 0?
(a) 127.
(b) 36.3.
(с) 114.
(d) 29.
37. What is the numerical value of Var (R1), the variance of the rank sum for d; > 0? You may ignore the
ties.
(a) 85.5.
(b) 999.
(с) 333
(d) 527.25.
38. Assume that a nonparametric sign test is performed to compare two groups. Let z, denote values from the first
group and yi denote values from the second group. If it is found that n = 36 with no ties, and the observed value
of the test statistic Zobs =, which is the correct value of C where C = the number of d, = 1, - y, > 0? Hint :
Take C >4.
(а) 20.
(b) 20.5.
(с) 21.
(d) 18.
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[Questions 39-40] Two geological formations are compared with respect to richness of their mineral content. The mineral
contents of 7 specimens of ore collected from each formation are measured by chemical analysis. The aim is to assess whether
these data provide evidence that the two formations have different mineral contents. Assume that the distributions of the
populations from which these specimens are collected are normal with equal variances.
Formation 1 () 7.6 | 11.1 | 6.8| 9.8 | 4.9 |
Formation 2 (r2) 7.9
6.1 15.1
6.4 | 4.1 | 13.2 3.9 | 3.7 5.2
I1 = 8.7714
S1 = 3.5099
I = 6.3429
S2 = 3.3847
39. What is the numerical value of the pooled variance?
(a) 10.1895.
(b) 3.4479.
(c) 5.8700.
(d) 11.8878.
40. If the observed value is 1.3177 what is the range of values that the p- value can take?
(a) 0.05 < p – value < 0.10.
(b) 0.01 <p - value < 0.025.
(c) 0.025 < p - value < 0.05.
(d) 0.1 <p- value < 0.25.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F555163de-6a8a-4e74-9393-f0165da49d9d%2F16de04d3-bc71-42b4-9553-dbfb10e5ba28%2F0scb057_processed.jpeg&w=3840&q=75)
Transcribed Image Text:[Questions 35-37] A study was conducted to assess whether there is a difference in two analgesic drugs (drug A and B) in
relieving pain in patients suffering from arthritis. Each of the 18 patients involved are given both of the drugs at an interval
sufficient to allow the effects of the earlier drug to clear before administering the second drug and the time it takes for the
pain to go away is recorded. A nonparametric approach is adopted as there were no reasonable grounds to assume normality.
The following table is provided as part of the analysis.
d -diff +diff | f. total f Ranks
Ave ranks
0.1
-0.1
1
1
1
0.2
-0.2
1
2
2
0.3
0.3
1
3
3
0.6
-0.6
1
4
0.7
-0.7
1
1
5
1.1
1.1
1
1
6
1.3
-1.3
1
7
1.5
1.5
2
2
8-9
8.5
1.8
1
1.8
2
3
10-12
10
11
12
13.5
15
16
2
2
1
1
13
2.1
2.1
1
1
14
2.3
2.3
15-16
2.6
2.6
17
12.4
12.4
1
1
18
35. Which is the correct set of hypotheses for this study?
(a) Ho : A4 = An vs Hị : AA# Ag.
(b) Ho : A = 0 vs H : A # 0.
(c) Hị : H4 vs Hị :44 = 0.
(d) Ho : HA = HB Vs H1 : µA HB-
36. What is the numerical value of R1, the rank sum for d, > 0?
(a) 127.
(b) 36.3.
(с) 114.
(d) 29.
37. What is the numerical value of Var (R1), the variance of the rank sum for d; > 0? You may ignore the
ties.
(a) 85.5.
(b) 999.
(с) 333
(d) 527.25.
38. Assume that a nonparametric sign test is performed to compare two groups. Let z, denote values from the first
group and yi denote values from the second group. If it is found that n = 36 with no ties, and the observed value
of the test statistic Zobs =, which is the correct value of C where C = the number of d, = 1, - y, > 0? Hint :
Take C >4.
(а) 20.
(b) 20.5.
(с) 21.
(d) 18.
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[Questions 39-40] Two geological formations are compared with respect to richness of their mineral content. The mineral
contents of 7 specimens of ore collected from each formation are measured by chemical analysis. The aim is to assess whether
these data provide evidence that the two formations have different mineral contents. Assume that the distributions of the
populations from which these specimens are collected are normal with equal variances.
Formation 1 () 7.6 | 11.1 | 6.8| 9.8 | 4.9 |
Formation 2 (r2) 7.9
6.1 15.1
6.4 | 4.1 | 13.2 3.9 | 3.7 5.2
I1 = 8.7714
S1 = 3.5099
I = 6.3429
S2 = 3.3847
39. What is the numerical value of the pooled variance?
(a) 10.1895.
(b) 3.4479.
(c) 5.8700.
(d) 11.8878.
40. If the observed value is 1.3177 what is the range of values that the p- value can take?
(a) 0.05 < p – value < 0.10.
(b) 0.01 <p - value < 0.025.
(c) 0.025 < p - value < 0.05.
(d) 0.1 <p- value < 0.25.
![[Questions 41-43] Suppose a clinical trial is conducted to test the efficacy of a new drug, spectinomycin, for treating gonor-
rhoea in females. Fifty patients are given a 4-g daily dose of the drug and are seen one week later, at which time 7 of the
patients still have gonorrhoea.
41. What is the best point estimate for p, the probability of failure with the drug?
(a) 0.08.
(b) 0.14.
(c) 0.86.
(d) 0.56.
.
42. Construct a 98% confidence interval for p, the probability of failure with the drug.
(a) (0.0438; 0.2362).
(b) j0.0259; 0.2541
(c) (0.0311; 0.2412].
(d) (0.0593; 0.2207).
43. Suppose we know penicillin G at a daily dose of 4.8 mega units has a 10% failure rate. Also, suppose that a 98%
CI for the probability of failure with the spectinomycin drug is given by [0.0311; 0.2412]. What can be said in
comparing the two drugs?
(a) Since 10% is within the given 98% interval, we would conclude that it is possible that the two drugs are not
significantly different.
(b) Since 10% is in the interval, we would conclude that it is possible that the two drugs are significan
(c) Since 10% is not in the interval, we would conclude that it is possible that the two drugs are significantly
different.
(d) Since 0 is in the interval, we would conclude that it is possible that the two drugs are equally effective.
different.
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44. If p - value = 0.02 for Ho : p = 0 vs Hị : p # 0, which statement is true at the 5% level of signifi-
сance?
(a) Ho will not be rejected.
(b) р> 1.
(c) The true correlation is non-significant.
(d) The true correlation is significant.
45. Suppose X N(ur = 15, o = = ). From this information, we are asked to determine P A= 0.99.
The value of a is given by:
13/21
(a) 14.0696.
(b) 13.9696.
(c) 15.9304.
(d) 18.7216.
46. Suppose an experiment is carried out with an interest in assessing if mean reaction time differ in 3 groups of people
after taking the respective beverages (water, fruit juice and coffee). The following diagrams are obtained by two
students as part of their projects.
Student A
Student B
Bongketa kr Readion Time to Beveras
Bee n T Be
30
24
28
22
26
24
20
22
16
14
14
12
12
10
10
Mean
DMeana
IMeanetSE
Juce
Coffee
Water
Juice
Cafee
OMean
IMeane1E
Beverage
Bereag
Which statement is true?
(a) H, will is more likely to be rejected by student B.
(b) Between group variability is larger for student A than between group variability.
(c) Within group variability is larger for student B than between group variability.
(d) Ho is more likely to be rejected by student A.
47. Given the following stem and leaf plot. What is the coefficient of variation?
Stem (units)
Leaf (hundredths)
6
47
7
13
42
8
50
29
53
9
15
77 09
60 70 54
10
28
43
16
87
11
35
61](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F555163de-6a8a-4e74-9393-f0165da49d9d%2F16de04d3-bc71-42b4-9553-dbfb10e5ba28%2Fcrsbct8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:[Questions 41-43] Suppose a clinical trial is conducted to test the efficacy of a new drug, spectinomycin, for treating gonor-
rhoea in females. Fifty patients are given a 4-g daily dose of the drug and are seen one week later, at which time 7 of the
patients still have gonorrhoea.
41. What is the best point estimate for p, the probability of failure with the drug?
(a) 0.08.
(b) 0.14.
(c) 0.86.
(d) 0.56.
.
42. Construct a 98% confidence interval for p, the probability of failure with the drug.
(a) (0.0438; 0.2362).
(b) j0.0259; 0.2541
(c) (0.0311; 0.2412].
(d) (0.0593; 0.2207).
43. Suppose we know penicillin G at a daily dose of 4.8 mega units has a 10% failure rate. Also, suppose that a 98%
CI for the probability of failure with the spectinomycin drug is given by [0.0311; 0.2412]. What can be said in
comparing the two drugs?
(a) Since 10% is within the given 98% interval, we would conclude that it is possible that the two drugs are not
significantly different.
(b) Since 10% is in the interval, we would conclude that it is possible that the two drugs are significan
(c) Since 10% is not in the interval, we would conclude that it is possible that the two drugs are significantly
different.
(d) Since 0 is in the interval, we would conclude that it is possible that the two drugs are equally effective.
different.
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STA 1S1/1P1: September 2021
page 13 of 21
44. If p - value = 0.02 for Ho : p = 0 vs Hị : p # 0, which statement is true at the 5% level of signifi-
сance?
(a) Ho will not be rejected.
(b) р> 1.
(c) The true correlation is non-significant.
(d) The true correlation is significant.
45. Suppose X N(ur = 15, o = = ). From this information, we are asked to determine P A= 0.99.
The value of a is given by:
13/21
(a) 14.0696.
(b) 13.9696.
(c) 15.9304.
(d) 18.7216.
46. Suppose an experiment is carried out with an interest in assessing if mean reaction time differ in 3 groups of people
after taking the respective beverages (water, fruit juice and coffee). The following diagrams are obtained by two
students as part of their projects.
Student A
Student B
Bongketa kr Readion Time to Beveras
Bee n T Be
30
24
28
22
26
24
20
22
16
14
14
12
12
10
10
Mean
DMeana
IMeanetSE
Juce
Coffee
Water
Juice
Cafee
OMean
IMeane1E
Beverage
Bereag
Which statement is true?
(a) H, will is more likely to be rejected by student B.
(b) Between group variability is larger for student A than between group variability.
(c) Within group variability is larger for student B than between group variability.
(d) Ho is more likely to be rejected by student A.
47. Given the following stem and leaf plot. What is the coefficient of variation?
Stem (units)
Leaf (hundredths)
6
47
7
13
42
8
50
29
53
9
15
77 09
60 70 54
10
28
43
16
87
11
35
61
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