MBA 503 University of Maryland University College Statistics Worksheet

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Mathematics

mba 503

University of Maryland University College

MBA

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QUESTION 1

The margin of error is always greater than or equal to the standard error.

True

False

3.4 points

QUESTION 2

A clinical trial is being conducted in order to determine the efficacy of a new drug used to treat Rheumatoid arthritis. The efficacy of the medication will not only be determined by the physical improvement of symptoms but also by using a blood test to examine the concentration C-reactive protein (an inflammatory marker) in an individual’s blood. If the researcher wants a margin of error for the level of C-reactive protein to be less than or equal to 3.0 mg/dL, and if the standard deviation for C-reactive protein concentrations among arthritis patients was previously documented at 8 mg/dL, how many patients should be recruited for each group in the study assuming a 95% confidence interval will be used to quantify the mean differences between the control group and the treatment group?

n
for the treatment group = 112; n for the control group = 111

n
for the treatment group = 56; n for the control group = 57

n
for the treatment group = 55; n for the control group = 55

n
for the treatment group = 112; n for the control group = 112

3.4 points

QUESTION 3

It is important for researchers to account for attrition or loss of participants during follow-up.

True

False

3.4 points

QUESTION 4

When performing a Mann-Whitney U test, one should always use the higher value of the calculated U values to compare to the critical U value while making the decision rule.

True

False

3.4 points

QUESTION 5

A researcher decides to take a random sample of the population and determine the ALT levels of the population, which fall on a continuum. A bar chart would be useful in determining if the ALT levels of the population are normally distributed.

True

False

3.4 points

QUESTION 6

Which of the following individuals is likely to be excluded from a clinical trial?

An individual with other diseases besides the disease of interest.

An individual whose data is considered to be an outlier.

An individual of who is considered to be a minority.

An individual who will have difficulty complying trial protocols.

3.4 points

QUESTION 7

A researcher notes that there seems to be a difference in the prevalence of high blood pressure among college-educated individuals who consume low amounts of processed foods and the prevalence of individuals who only have a high school education and consume high amounts of processed foods. Use the appropriate hypothesis to test for the independence of the two independent variables presented here at the 5% significance level to ensure confounding has not influenced the study’s results. Then, interpret your response.

Diet Low in Processed Foods

Normal BP

High BP

Total

College Education

124

55

179

High School Education

69

152

221

Total

193

207

400

Diet High in Processed Foods

Normal BP

High BP

Total

College Education

64

85

149

High School Education

98

153

251

Total

162

238

400

The chi square value of 37.724 is higher than the chi square value of 3.84; therefore, we do not reject H0 at the 5% level and reject H1, which states that level of education and the amount of processed foods in an individual’s diet are not independent of one another.

The chi square value of 37.724 is higher than the chi square value of 3.84; therefore, we do not reject H0 at the 5% level and reject H1, which states that level of education and the incidence of high blood pressure are not independent of one another.

The chi square value of 37.724 is higher than the chi square value of 3.84; therefore, we can reject H0 at the 5% level in favor of H1, which states that level of education and the incidence of high blood pressure are not independent of one another.

The chi square value of 37.724 is higher than the chi square value of 3.84; therefore, we can reject H0 at the 5% level in favor of H1, which states that level of education and the amount of processed foods in an individual’s diet are not independent of one another.

3.4 points

QUESTION 8

If a test is run and p = 0.0356, then we can reject H0 at a = 0.01.

True

False

3.4 points

QUESTION 9

The sample size required to detect an effect size of 0.25 is larger than the sample size required to detect an effect size of 0.50 with 80% power and a 5% level of significance.

True

False

3.4 points

QUESTION 10

In logistic regression, the predictors are dichotomous, and the outcome is a continuous variable.

True

False

3.4 points

QUESTION 11

Researchers use active-controlled trials to test new medications that are used to treat a particular illness against old medications used to treat the same illness.

True

False

3.4 points

QUESTION 12

Assume a doctor uses a specific form of mesh to repair all hernias in his hernia patients. The makers of the mesh found there was an error that occurred while making the mesh, and the hernia mesh has a 45% chance of failure. The doctor has treated 7 patients with the mesh so far; thus, the probability that the mesh does not fail in all seven patients is .0152.

True

False

3.4 points

QUESTION 13

A researcher wants to compare the mean concentration of two medications considered biologically equivalent, i.e., two medications that are able to produce the same therapeutic effect at the same level of concentration in the blood. The group of individuals on medication one (n = 32) had a mean blood concentration of 21.7 micrograms per milliliter with a standard deviation of 8.7 micrograms per milliliter. The group of individuals on medication two (n
= 32) had a mean blood concentration of 19.4 micrograms per milliliter with a standard deviation of 5.2 micrograms per milliliter. Construct and interpret a 95% confidence interval demonstrating the difference in means for the individuals on medication one when compared to the group of individuals on medication two.

The researchers are 95% confident that the true mean difference in medication concentration levels between individuals on medication one and individuals on medication two is between 4.867 micrograms per milliliter and 9.467 micrograms per milliliter.

The researchers are 95% confident that the true mean difference in medication concentration levels between individuals on medication one and individuals on medication two is between -1.212 micrograms per milliliter and 5.812 micrograms per milliliter.

The researchers are 95% confident that the true mean difference in medication concentration levels between individuals on medication one and individuals on medication two is between 11.747 micrograms per milliliter and 16.347 micrograms per milliliter.

The researchers are 95% confident that the true mean difference in medication concentration levels between individuals on medication one and individuals on medication two is between 3.477 micrograms per milliliter and 8.077 micrograms per milliliter.

3.4 points

QUESTION 14

Considering the data blow. The mean is 118.44.
100 120 111 115 120 116 125 129 130

True

False

3.4 points

QUESTION 15

Randomization in a clinical trial is defined as which of the following?

The process by which individuals are coupled into groups for comparison in order to minimize bias and confounding.

The process by which individuals are assigned a number and are selected through the usage of a pattern which minimizes bias and confounding.

The process by which individuals are randomly assigned to a treatment or control group which minimizes bias and confounding.

The process by which individuals are asked to volunteer for a study which minimizes bias and confounding.

3.4 points

QUESTION 16

A stratified random sample can be used to ensure underrepresented populations are represented in a study.

True

False

3.4 points

QUESTION 17

A researcher wants to determine the sensitivity of mammograms to determine how effective they are at diagnosing women who have breast cancer. Assume the researcher obtained the above results from a study, calculate and interpret the sensitivity of mammograms for detecting breast cancer.

Frequency of Breast Cancer Cases

Frequency of Non-Cancer Cases

Frequency of Individuals Who Screened Positive

17

5

Frequency of Individuals Who Screened Negative

8

77

A total of 66.67% of individuals who have breast cancer test positive for breast cancer when using a mammogram as the primary diagnostic test for breast cancer.

A total of 68% of individuals who have breast cancer test positive for breast cancer when using a mammogram as the primary diagnostic test for breast cancer.

A total of 70.59% of individuals who have breast cancer test positive for breast cancer when using a mammogram as the primary diagnostic test for breast cancer.

A total of 92.77% of individuals who have breast cancer test positive for breast cancer when using a mammogram as the primary diagnostic test for breast cancer.

3.4 points

QUESTION 18

The level of significance is the probability that we reject the null hypothesis (in favor of the alternative) when it is actually true.

True

False

3.4 points

QUESTION 19

Ethnicity is best described as which type of variable?

Dichotomous variable

Ordinal variable

Categorical variable

Continuous variable

3.4 points

QUESTION 20

If a 90% confidence interval for the mean is (75.3 to 80.9), we would reject H0: m =70 in favor of H1: m ≠ 70 at a = 0.05.

True

False

3.4 points

QUESTION 21

If a 95% confidence interval for the difference in two independent means is (-4.5 to 2.1), then the point estimate is -2.1.

True

False

3.4 points

QUESTION 22

The level of significance alpha most commonly used are: 0.01, 0.05, 0.1.

True

False

3.4 points

QUESTION 23

Considering the data blow. The median is 120.
100 120 111 115 120 116 125 129 130

True

False

3.4 points

QUESTION 24

Assuming 50,000 individuals in the United States are diagnosed every year, and of those individuals diagnosed with HIV each year, approximately 33,500 individuals diagnosed with HIV are gay or bisexual males. What prevalence of the new HIV cases are from members of the population of gay or bisexual males?

0.67%

6.70%

33.0%

67.0%

3.4 points

QUESTION 25

If a 95% confidence interval for the difference in two independent means is (2.1 to 4.5), there is no significant difference in means.

True

False

3.4 points

QUESTION 26

A clinical trial is conducted to compare an experimental medication to placebo to reduce the symptoms of asthma. Two hundred participants are enrolled in the study and randomized to receive either the experimental medication or placebo. The primary outcome is self-reported reduction of symptoms. Among 100 participants who receive the experimental medication, 38 report a reduction of symptoms as compared to 21 participants of 100 assigned to placebo. When you test if there is a significant difference in the proportions of participants reporting a reduction of symptoms between the experimental and placebo groups. Use α = 0.05. What should the researcher’s conclusion be for a 5% significance level? Reject H0
because 2.64 ≥ 1.960. We have statistically significant evidence at α = 0.05 to show that there is a difference in the proportions of patients reporting a reduction in symptoms.

We reject H0 at the 5% level because 2.64 is greater than 1.96. We do have statistically significant evidence at α = 0.05 to show that there is a difference in the proportions of patients reporting a reduction in symptoms.

We fail to reject H0 at the 5% because -2.64 is less than 1.645. We do not have statistically significant evidence to show that there is a difference in the proportions of patients reporting a reduction in symptoms.

We fail to reject H0 at the 5% because -2.64 is less than 1.96. We do have statistically significant evidence at α = 0.05 to show that there is a difference in the proportions of patients reporting a reduction in symptoms.

We fail to reject H0 at the 5% because 2.64 is greater than -1.645. We do have statistically significant evidence at α = 0.05 to show that there is a difference in the proportions of patients reporting a reduction in symptoms.

3.4 points

QUESTION 27

An r value of .8 indicates a strong positive correlation.

True

False

3.4 points

QUESTION 28

The following are body mass index (BMI) scores measured in 12 patients who are free of diabetes and are participating in a study of risk factors for obesity. Body mass index is measured as the ratio of weight in kilograms to height in meters squared. Generate a 95% confidence interval estimate of the true BMI.

25 27 31 33 26 28 38 41 24 32 35 40

3.4 points

QUESTION 29

How many subjects would be needed to ensure that a 95% confidence interval estimate of BMI had a margin of error not exceeding 2 units?

25 27 31 33 26 28 38 41 24 32 35 40

3.4 points

QUESTION 30

Based on the data set below , what is the standard deviation?

25 27 31 33 26 28 38 41 24 32 35 40

3.4 points

QUESTION 31

Peak expiratory flow (PEF) is a measure of a patient’s ability to expel air from the lungs. Patients with asthma or other respiratory conditions often have restricted PEF. The mean PEF for children free of asthma is 306. An investigator wants to test whether children with chronic bronchitis have restricted PEF. A sample of 40 children with chronic bronchitis is studied, and their mean PEF is 279 with a standard deviation of 71. Is there statistical evidence of a lower mean PEF in children with chronic bronchitis? Run the appropriate test at a = 0.05.

3.4 points

QUESTION 32

Peak expiratory flow (PEF) is a measure of a patient’s ability to expel air from the lungs. Patients with asthma or other respiratory conditions often have restricted PEF. The mean PEF for children free of asthma is 306. An investigator conducts a study to investigate whether there is a difference in mean PEF in children with chronic bronchitis as compared to those without asthma or other respiratory conditions often have restricted PEF. Data on PEF are collected and summarized below. Based on the data, is there statistical evidence of a lower mean PEF in children with chronic bronchitis as compared to those without? Run the appropriate test at a = 0.05.

Group

Number of Children

Mean PEF

Std Dev PEF

Chronic Bronchitis

25

281

68

No Chronic Bronchitis

25

319

74

3.4 points

QUESTION 33

A clinical trial is run to investigate the effectiveness of an experimental drug in reducing preterm delivery to a drug considered standard care and to a placebo. Pregnant women are enrolled and randomly assigned to receive either the experimental drug, the standard drug or a placebo. Women are followed through delivery and classified as delivering preterm (< 37 weeks) or not. The data are shown below.

Preterm Delivery

Experimental Drug

Standard Drug

Placebo

Yes

17

23

35

No

83

77

65

Is there a statistically significant difference in the proportions of women delivering preterm among the three treatment groups? Run the test at a 5% level of significance.

3.4 points

QUESTION 34

A study is run comparing HDL cholesterol levels between men who exercise regularly and those who do not. The data are shown below.

Regular Exercise

N

Mean

Std Dev

Yes

35

48.5

12.5

No

120

56.9

11.9

Generate a 95% confidence interval for the difference in mean HDL levels between men who exercise regularly and those who do not.

3.4 points

QUESTION 35

Suppose a hypertension trial is mounted and 18 participants are randomly assigned to one of the comparison treatments. Each participant takes the assigned medication and his or her systolic blood pressure is recorded after 6 months on the assigned treatment. The data are as follows.

Standard Treatment

Placebo

New Treatment

124

134

114

111

143

117

133

148

121

125

142

124

128

150

122

115

160

128

  1. Is there a difference in mean systolic blood pressure among treatments? Run the appropriate test at α = 0.05.

3.4 points

QUESTION 36

A study is designed to investigate whether there is a difference in response to various treatments in patients with Rheumatoid arthritis. The outcome is the patient’s self-reported effect of treatment. The data are shown below. Is there a significant difference in effect of treatment? Run the test at a 5% level of significance.

Symptoms

Worsened

No Effect

Symptoms Improved

Total

Treatment 1

22

14

14

50

Treatment 2

14

15

21

50

Treatment 3

9

12

29

50

3.4 points

QUESTION 37

Using the data below, suppose we focus on the proportions of patients who show improvement. Is there a statistically significant difference in the proportions of patients who show improvement between treatments 1 and 2. Run the test at a 5% level of significance.

Symptoms

Worsened

No Effect

Symptoms Improved

Total

Treatment 1

22

14

14

50

Treatment 2

14

15

21

50

Treatment 3

9

12

29

50

3.4 points

QUESTION 38

An analysis is conducted to compare mean time to pain relief (measured in minutes) under four competing treatment regimens. Summary statistics on the four treatments are shown below.

Treatment

Sample Size

Mean Time to Relief

Sample Variance

A

5

33.8

17.7

B

5

27.0

15.5

C

5

50.8

9.7

D

5

39.6

16.8

Complete the following ANOVA Table.

Source of Variation

SS

df

MS

F

Between Groups

.

Within Groups

3719.48

Total

3.4 points

QUESTION 39

A small pilot study is conducted to investigate the effect of a nutritional supplement on total body weight. Six participants agree to take the nutritional supplement. To assess its effect on body weight, weights are measured before starting the supplementation and then after 6 weeks. The data are shown below. Is there a significant increase in body weight following supplementation? Run the test at a 5% level of significance.

Subject

Initial Weight

Weight after 6 Weeks

1

155

157

2

142

145

3

176

180

4

180

175

5

210

209

6

125

126

3.4 points

QUESTION 40

A small pilot study is run to compare a new drug for chronic pain to one that is currently available. Participants are randomly assigned to receive either the new drug or the currently available drug and to report improvement in pain on a 5-point ordinal scale: 1 = Pain is much worse, 2 = Pain is slightly worse, 3 = No change, 4 = Pain improved slightly, 5 = Pain much improved. Is there a significant difference in self-reported improvement in pain? Use the Mann-Whitney U test with a 5% level of significance.

New Drug: 4 5 3 3 4 2

Standard Drug: 2 3 4 1 2 3

3.4 points

QUESTION 41

The following table was presented in an article summarizing a study to compare a new drug to a standard drug and to a placebo.

Characteristic*

New Drug

Standard Drug

Placebo

p

Age, years

45.2 (4.8)

44.9 (5.1)

42.8 (4.3)

0.5746

% Female

51%

55%

57%

0.1635

Annual Income, $000s

59.5 (14.3)

63.8 (16.9)

58.2 (13.6)

0.4635

% with Insurance

87%

65%

82%

0.0352

Disease Stage

0.0261

Stage I

35%

18%

33%

Stage II

42%

37%

47%

Stage III

23%

51%

20%

*Table entries and Mean (Sd. or %

Are there any statistically significant differences in the characteristics shown among the treatments? Justify your answer

3.5 points

QUESTION 42

What is the appropriate statistical test to assess whether there is an association between obesity status (normal weight, overweight, obese) and 5-year incident cardiovascular disease (CVd.? Suppose each participant’s obesity status (category) is known along with whether they develop CVD over the next 5 years or not.

3.5 points

QUESTION 43

A random sample of 8 adults aged 30 years were asked how much they spent on medical costs in the year 2009. Using the following data, compute the sample mean, the sample standard deviation, the sample median, and the first and third quartiles. 300 140 5600 520 470 700 640 1200

3.5 points

QUESTION 44

The table below summarizes baseline characteristics of patients participating in a clinical trial. a) Are there any statistically significant differences in baseline characteristics between treatment groups? Justify your answer.

Characteristic

Placebo (n = 125)

Experimental ( n =125)

P

Mean (+ Sd. Age

54 + 4.5

53 + 4.9

0.7856

% Female

39%

52%

0.0289

% Less than High School Education

24%

22%

0.0986

% Completing High School

37%

36%

% Completing Some College

39%

42%

Mean (+ Sd. Systolic Blood Pressure

136 + 13.8

134 + 12.4

0.4736

Mean (+ Sd. Total Cholesterol

214 + 24.9

210 + 23.1

0.8954

% Current Smokers

17%

15%

0.5741

% with Diabetes

8%

3%

0.0438

3.5 points

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Explanation & Answer:
44 Questions
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Explanation & Answer

Attached.

QUESTION 1
The margin of error is always greater than or equal to the standard error.
True
False
3.4 points

QUESTION 2
A clinical trial is being conducted in order to determine the efficacy of a new drug used to treat Rheumatoid
arthritis. The efficacy of the medication will not only be determined by the physical improvement of
symptoms but also by using a blood test to examine the concentration C-reactive protein (an inflammatory
marker) in an individual’s blood. If the researcher wants a margin of error for the level of C-reactive protein
to be less than or equal to 3.0 mg/dL, and if the standard deviation for C-reactive protein concentrations
among arthritis patients was previously documented at 8 mg/dL, how many patients should be recruited for
each group in the study assuming a 95% confidence interval will be used to quantify the mean differences
between the control group and the treatment group?
n
for the treatment group = 112; n for the control group = 111
n
for the treatment group = 56; n for the control group = 57
n
for the treatment group = 55; n for the control group = 55
n
for the treatment group = 112; n for the control group = 112

3.4 points

QUESTION 3
It is important for researchers to account for attrition or loss of participants during follow-up.
True
False
3.4 points

QUESTION 4
When performing a Mann-Whitney U test, one should always use the higher value of the calculated U values
to compare to the critical U value while making the decision rule.
True
False
3.4 points

QUESTION 5
A researcher decides to take a random sample of the population and determine the ALT levels of the
population, which fall on a continuum. A bar chart would be useful in determining if the ALT levels of the
population are normally distributed.
True

False
3.4 points

QUESTION 6
Which of the following individuals is likely to be excluded from a clinical trial?
An individual with other diseases besides the disease of interest.
An individual whose data is considered to be an outlier.
An individual of who is considered to be a minority.
An individual who will have difficulty complying trial protocols.

3.4 points

QUESTION 7
A researcher notes that there seems to be a difference in the prevalence of high blood pressure among
college-educated individuals who consume low amounts of processed foods and the prevalence of individuals
who only have a high school education and consume high amounts of processed foods. Use the appropriate
hypothesis to test for the independence of the two independent variables presented here at the 5%
significance level to ensure confounding has not influenced the study’s results. Then, interpret your response.
Diet Low in Processed Foods

College
Education
High School
Education
Total

Normal BP

High BP

Total

124

55

179

6...


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