# Statistics- Suppose you wish to compare the mean years of education

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

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.

Question 3
Ethnicity of USF students is

Discrete
Continuous
Qualitative
None of the above

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

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

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

Question 7
A sample of 1000 subjects is stratified gender and physical activity level as follows:

Gender
Male
Female
Total

Physical Activity Level
Low
High
100
500
200
200
300
700

Total
600
400
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

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

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
+
Total
0.84
0.87
0.90

Yes
270
30
300
0.80

Pregnant?
No
40
160
200

Total
310
190
500

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
p(x)

0
0.55

1
0.25

2
0.15

3
0.05

The probability that less than two of the classes are full at the time of registration [P(X < 2)] is equal to

0.30
0.70
0.80
0.95

Question 11
The central limit theorem tells us that the sampling distribution of the sample mean is approximately normal.
Which of the following conditions are necessary for the theorem to be valid:

a) The sample size has to be large.
b) We have to be sampling from a normal population.
c) The population has to be symmetric.
d) Both a) and c).

Question 12
Which of the following statements are true regarding Type I or Type II errors?

Type II error occurs when we fail to reject a true null hypothesis.
Type II error occurs when we fail to reject a false alternative hypothesis.
Type-I error occurs when we reject a true null hypothesis
Type-I error occurs when we reject a true alternative hypothesis.

Question 13
In One Sample Proportion test, it is important to convert the sample proportion to a z-score first. In this
example, we selected a random sample of size 110 from a pool of university students and asked whether they
use the university gym on a regular basis. Sixty-eight replied yes. Assuming that the population proportion
under the null hypothesis is 50%, what is the z-score for the sample proportion?

2.48
2.63
3.27
3.38

Question 14
To investigate the prevalence rate of diabetes among men in Florida, we drew a random sample of 70 men
from that population and among them 15 people had diabetes. For the following hypotheses, what would be
your conclusion based on the information provided? The level of significance (alpha level) is 0.05. (Hint:
Depending on the direction of the alternative test, use 1.96 or -1.96 as the critical z-value)
Ho: P = 0.2 (Null)
Ha: P > 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.

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

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

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]

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

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

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

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

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

Question 23
Which of the following indicates a weak positive correlation?

-.81
0
.35
.93

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.

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