# STATS Final Exam MCQs

August 30, 2017

Question
Question 1
Suppose you wish to compare the mean years of education of all faculty in the Epidemiology and Biostatistics department to the mean years of education of all faculty in the Community and Family Health department at USF. Which is the most appropriate technique for gathering the needed data?

Randomized trial
Sample survey
Experiment
Census

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Question 2
In a study on the effect of calcium on bone density levels, 50 women were randomly chosen to receive calcium and 50 were chosen to receive a placebo. These subjects were later examined to check for differences in their bone density levels. In a second study on the effect of a new combination drug of calcium and vitamin D on bone density, 100 subjects were randomly chosen to receive the new medication and 100 were chosen to receive a placebo. The subjects were later examined to check for differences in their bone density levels.
Which of the following statements is correct?

The first study was a controlled experiment, while the second was an observational study.
The first study was an observational study, while the second was controlled experiment.
Both studies were controlled experiments.
Both studies were observational studies.

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Question 3
Ethnicity of USF students is

Discrete
Continuous
Qualitative
None of the above

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Question 4
Which of the following methods of sample data is not appropriate for determining the shape of a frequency distribution for the variable height (measured in inches)?

Box plot
Pie chart
Stem-and leaf display
All of the above

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Question 5
A researcher would like to study BMI levels in adults 20-40 years of age. She selected 9 patients and found their BMI values to be: 18, 29, 20, 22, 25, 27, 26, 30, 37
The mean BMI level of this group of patients is
25.8
26.0
26.2
27.9

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Question 6
A researcher would like to study BMI levels in adults 20-40 years of age. She selected 9 patients and found their BMI values to be: 26, 20, 18, 32, 29, 38, 21, 25, 23
The standard deviation of BMI levels of this group of patients is

5.7
5.9
6.4
6.6

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Question 7
A sample of 1000 subjects is stratified gender and physical activity level as follows:
Physical Activity Level
Gender Low High Total
Male 100 500 600
Female 200 200 400
Total 300 700 1000

In a random selection of a subject from the study population, what is the probability that the person is female?

3/10
7/10
3/5

2/5

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Question 8
The Table below shows data on age group by smoking status that was collected by a study looking at the associations between smoking and age. What is the probability of selecting a former smoker between the ages of 61 to 70?

0.030
0.048
0.073
0.085

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Question 9
Five hundred women are enrolled in a study to evaluate the accuracy of a test for pregnancy. 300 of the women were actually pregnant. 270 of the pregnant women had a positive test as did 40 of the women who were not pregnant. What is the probability (i.e., specificity) that a woman tested negative on a test given that she is not pregnant?
Test Pregnant?
Yes No Total
+ 270 40 310
– 30 160 190
Total 300 200 500

0.80
0.84
0.87
0.90

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Question 10
A graduate student is registering for 3 courses in one semester. X=the number of courses that are full at the time of registration. The random variable X has a probability distribution as follows
x 0 1 2 3
p(x) 0.55 0.25 0.15 0.05
The probability that less than two of the classes are full at the time of registration [P(X 0.2 (Alternative)

Reject the null hypothesis.
Fail to reject the null hypothesis.
Cannot conclude due to the sample size and the population proportion not meeting the requirement needed for applying Central Limit Theorem.
Cannot conclude due to lack of information.

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Question 15
Researchers want to test the effectiveness of a new pain medication. Four hundred people were recruited to participate in the clinical trial. In clinical testing, 48 out of 180 people taking the medication reported pain symptoms. Of the other 220 people receiving a placebo, 87 reported pain symptoms. What is the estimated standard error of the difference of the two sample proportions based on pooled sample proportion?

0.038
0.041
0.043
0.047

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Question 16
It is known that the population standard deviation of weight among females is 30. Assuming that we have a random sample of 210, what is the standard error of the average weight among women of a sample of this size?

1.29
2.07
2.20
2.72
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Question 17
It is known that the population standard deviation of weight among females is 15. Assuming that we have a random sample of 136 and a sample mean of 125, what would be your 90% confidence interval estimate of the population mean weight? (Hint: use 1.65 as the critical z-value)

[122.9, 127.1]
[121.9, 130.4]
[123.7, 133.5]
[125.7, 133.6]

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Question 18
Ten students were randomly selected from the College of Public Health and their diastolic blood pressure was tested. The sample mean and standard deviation were 78.2 mmHg and 2.1 mmHg respectively. What is the obtained t-score for this sample under the null hypothesis Ho: µ = 80?

-1.57
1.55
-2.71
2.60

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Question 19
To compare the treatment effects of two interventions, two independent samples of patient medical data were collected. The sample sizes are 25 and 21 respectively. Assuming that the two populations shared the same variance, the researchers decided to conduct a two independent samples test for the means. What would be the number of degrees of freedom for the obtained t statistic with these sample sizes?

44
47
50
52

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Question 20
Researchers want to test the effectiveness of a new pain medication. Four hundred people were recruited to participate in the clinical trial. In clinical testing, 49 out of 210 people taking the medication reported pain symptoms. Of the other 190 people receiving a placebo, 140 reported pain symptoms. Combining the two samples together, what is the overall proportion of those who reported pain symptoms among all participants?

0.19
0.34
0.45
0.47

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Question 21
For correlation coefficients, which of the following is true?

The closer r is to 1, the stronger the negative linear relationship
The closer r is to 1, the stronger the positive linear relationship
The closer r is to 0, the stronger the positive linear relationship
The closer r is to -1, the strong the positive linear relationship

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Question 22
Which of the following assumptions concerning the probability distribution of the random error term in a simple regression model is stated incorrectly?

The distribution is normal
The mean of the distribution is 1
The errors are independent from one value of y to the next
The variance of the distribution is constant
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Question 23
Which of the following indicates a weak positive correlation?

-.81
0
.35
.93

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A biostatistician finds the relationship between the number of weeks (X) spent in a hospital and number of seizures per week (Y) and is described by the following equation: y hat = 14.9 – 0.91x. This is based on a sample size of 50 patients and the associated coefficient of correlation is r = -.93.
Using this information above, answer the following question: How do you interpret r = -.93?

There is a perfect positive relationship between the number of weeks spent in a hospital and the number of seizures recorded.
There is a perfect negative relationship between the number of weeks spent in a hospital and the number of seizures recorded.
There is a strong negative relationship between the number of weeks spent in a hospital and the number of seizures recorded.
There is a strong positive relationship between the number of weeks spent in a hospital and the number of seizures recorded.

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Question 25
The probability that a person tested positive on a screening test given that he/she has a disease is called the

Negative predictive value
Positive predictive value
Sensitivity
Specificity

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