PH 614 Mit term exam March 24-29 2022

QUESTION 1

1. For a certain population, systolic BP is normally distributed with =114 and =13.Hypertension is defined as systolic BP over 140 mmHg.

a. What is the z-score for systolic BP of 140, given this information?You may enter the Z-score rounded to the nearest integer (e.g.9) or to rounded to one decimal place (e.g.9.0). z=

b. What percentage of the population is hypertensive(Z>140)? You may use the Empirical Rule. %

4 points

QUESTION 2

1. For a population with blood pressure (BP) that follows a normal distribution with=114 and=13, suppose we randomly samplen=169 individuals from this population.What is the probability that the sample mean of systolic BP obtained from this sample will be between 115 and 116 mmHg? It is recommended to first compute the standard error, then compute the Z-scores for 115 and 116, then compute the difference between the cumulative probabilities associated with these two Z-scores..

		0.136
		0.864
		0.841
		0.977

4 points

QUESTION 3

1. The probability of success for a new experimental treatment is0.80in women.Assuming the same probability of success applies to men,a new trial is conducted to test the treatment in a sample of6men.Note that this defines a binomial random variable.
   1. What is theminimumnumber of possible successes?
   2. What is themaximumnumber of possible successes?
   3. What is theexpectednumber of successes? Report to one decimal place, such as 1.2.

3 points

QUESTION 4

1. Continuing from the previous question where the probability of success is0.80, what is the probability of observing exactly 6 successful treatments in your sample of 6 men?

		0.26
		4.8
		0.015
		0.026

4 points

QUESTION 5

1. Continuing from the previous question where the probability of success is0.80, what is the probability of observing less than 6 successful treatments in yoursample of 6 men? (hint: the answer is a natural extension of the answer from the previous question)

		0.74
		0.26
		0.15
		1.0

2 points

QUESTION 6

1. Before beginning a study investigating the ability of the drug heparin to prevent bronchoconstriction, baseline values of pulmonary function were measured for a sample of 14 individuals with a history of exercise-induced asthma. The mean value of forced vital capacity (FVC) for the sample was 4.49 liters and the standard deviation was 0.83 liters. The investigators reported the following 95% confidence interval for true mean FVC: 4.49 0.48.

a.What is the point estimate of true mean FVC?

b.What is the margin of error?

2 points

QUESTION 7

1. Interpret the meaningof "The95% confidence interval for true meanforced vital capacity (FVC) is4.49 0.48."

Choose one.

		We are 95% confident that the true population mean forced vital capacity (FVC) is between 4.01 and 4.97. In the long run, a confidence interval constructed this way will capture the true value of95% of the time.
		The true population mean forced vital capacity (FVC) is between 4.01 and 4.97.
		In the long run, a confidence interval constructed this way will capture the true value of99% of the time.
		The margin of error =0.96

3 points

QUESTION 8

1. Researchers are interested in estimating the prevalence of hypertension in a population of adults aged 40-65 from a particular community.Suppose the national prevalence in this population is 37.5% (p=0.375). The research team has enrolled n=167 participants.

The expected number ofhypertensive adults in this sample, rounded to the nearest integer = .

The expectednumber ofadults in this sample who are nothypertensive= .

Can the distribution of hypertensive adults be approximated by the normal distribution, given this sample? (yes or no)

3 points

QUESTION 9

1. Inthe study from the previousquestion,x=79 adults have been confirmed hypertensiveoutof n=167 participants.Assuming the standard normal distribution can be applied and p=0.375 under the null hypothesis,what is the Z-statistic for x=79? Recall that the expected value =npandthestandard deviation =.

		2.62
		6.26
		-1.96
		1.0

5 points

QUESTION 10

1. Continuingfromthepreviousquestion,if we randomly re-samplen=167 adults from thesame community, we willdefinitelyget79 confirmed hypertensive adults again.

True

False

2 points

QUESTION 11

1. Continuingfromthepreviousquestion,if we observed75hypertensive adultsin a randomsample of167,what is the one-sidedp-value associated with x=75,given the prevalence of 0.375under the null hypotheses?Recall, theone-sidedp-value =Pr(X >75).

		0.024
		0.976
		1.98
		-0.024

4 points

QUESTION 12

1. Consider the following two"exposure/outcome"scenarios.Computethe relative risk and risk difference for each,then submit your answers through the matching question.

SCENARIO A

.

SCENARIO B

- A. B. C. D.	Scenario Arelative risk (RR)
- A. B. C. D.	Scenario Arisk difference (RD)
- A. B. C. D.	Scenario Brelative risk (RR)
- A. B. C. D.	Scenario Brisk difference (RD)

A.	1.67
B.	1.65
C.	2%
D.	26%

8 points

QUESTION 13

1. Continuingfrom the lastquestion, which exposure scenario presents the greatest populationimpact?

		ScenarioB
		ScenarioA

2 points

QUESTION 14

1. A randomized controlled trial of supported employment among veterans with Posttraumatic Stress Disorder (PTSD)examined rates of competetive employmentfor veterans receivingindividual placement and support (IPS) supported employment (n=42), compared to veterans receiving a treatment as usual, namely Veterans Health Administration Vocational Rehabilitation Program (VRP) (n=43).

Table 2 shows the distribution of baseline characteristic by group. This was adapted fromDavis et al. 2012.Psychiatric services, 63(5):464-70.

Using= 0.05 as the decision rule (max allowable type 1 error is 5%), were there significant differences between groups in terms of:

a) Gender Type Y for Yes, N for No

Justification: test Type T for t-test, C for Chi-square test, p-value

b) Education Type Y for Yes, N for No

Justification: test Type T for t-test, C for Chi-square test, p-value

c) Posttraumatic Stress severity, as measured by CAPS Type Y for Yes, N for No

Justification: test Type T for t-test, C for Chi-square test, p-value

d) Disability level, as measured by WHODAS II Type Y for Yes, N for No

Justification: test Type T for t-test, C for Chi-square test, p-value

8 points

QUESTION 15

1. With respect to the previous questions,are you surprised to see such results?

		Yes, because this study was a randomized clinical trial.
		No, because this study was arandomizedclinical trial.
		Cannot determine

2 points

QUESTION 16

1. The study cited in the earlier questionreported that: "Thirty-two of the 42 IPS participants (76%) gained competitive employment, compared with 12 of the 43 VRP participants (28%) (2=19.84,df=1, p<.001). That is, veterans with PTSD who participated in IPS were 2.7 times more likely to gain competitive employment than those who received VRP."

a) Is the rate ofcompetitive employment significantly different between the IPS vs. VRP groups? Type Y for Yes, N for No

Justification: test Type T for t-test, C for Chi-square test, p-value

b) Is 2.7 a relative risk or odds ratio estimate? Type RR for Relative Risk, OR for Odds ratio. Hint: compute both RR and OR to answer this question.

5 points

QUESTION 17

1. As an observational study, a cohort of patients are obtained from the Department of Veterans Affairs hospital database.

A mutivariablelinear model is constructed to find acombination of independent variablesthat are all statistically significantly associated with mortality within a year of release (dependent variable) from a VA hospital after treatment for stroke.

Is this a predictive or explanatory model?

		Explanatory
		Predictive

3 points

QUESTION 18

1. Data from a randomizedcontrol trial are analyzed though a multivariablelogistic regression model in order to quantify the effect ofa specific diet on the odds of a cardiovascular disease event within the past five years, after adjusting for both the age and gender of each individual.

Is this a predictive or explanatory model?

		Predictive
		Explanatory

3 points

QUESTION 19

1. Suppose a researcher is interested in the effectiveness of a new anti-hypertensive medication in a sample of 28 clinical trial participants with high blood pressure, as measured bysystolic blood pressure in millimeters of mercury (mm Hg).In a pre/post study, the researchers decide to use each participant as their own control, offering participants the drug either before or after a control period that applies the current standard of care.The difference in systolic blood pressure between the new drug treatment and the standard of care control yielded a mean of -26 mm and a standard deviation of 10.9 mm.

Which one of the following is the appropriate approach to test if blood pressure under the new drug treatment is different than under the standard of care control?

		t-test for two independent samples
		Z-test for the difference between two proportions
		An inter-quartile range
		t-test for a paired (matched) sample

1 points

QUESTION 20

1. Continuing from the last question, which of the following is the 95% confidence interval of the mean difference?

		(-30.2, -21.8)
		(1.61, 11.39)
		(-29.5, -22.5)
		(-30.2, 21.8)

2 points

QUESTION 21

1. In a study examining socioeconomic differences in birthweight, the mean birthweight for babies born to n₁=41 mothers with a college education was 3145 grams with a standard deviation of 250 grams, while the mean birthweight for babies born to n₂=47 mothers with no more than a high school education was 2989 grams with a standard deviation of 329 grams

Which of the following states the appropriate hypotheses for testing if the mean birth weight between these two groups of mothers isdifferent, where₁= the mean for mothers with a college education and₂= the mean mothers with no more than a high school education

		H0:1=2vs. Ha:1 >
		H0:1=2vs. Ha:1 <2
		H0:12vs. Ha:1 >2
		H0:1=2vs. Ha:12

2 points

QUESTION 22

1. Continuingfrom the last question, which of the following is the 95% confidence interval for the difference between the mean birthweights of these two groups of mothers?

For calculating the standard error, use , recalling thats²is the sample variance, or standard deviation squared.

		(-33, 279.0)
		(-1.99, 1.99)
		(31.0, 281.0)
		(0.49, 257.0)

5 points

QUESTION 23

1. A study is conducted on a sample of people to investigate the association between age and total serum cholesterol.The correlation is estimated atr= 0.35 and the following summary statistics are available:

	sample mean	sample standard deviation
total cholesterol	202.8	38.4
age	44.3	10.0

2. Which one of thefollowingbest describes the dependence of total serum cholesterol (Y variable) on age (X variable).[Hint:Use the numbers provided to compute the slope and then the intercept of a linear model.]

		y=202.8+ 44.3x
		y =143.26+ 1.34x
		y=1.34+ 143.26x

5 points

QUESTION 24

1. Researchers at an infectious disease clinic hypothesize that early mortality is strongly associated with heroin use in their HIV positive patient population.In order to better assess this relationship, the researchers decided to control forage and gender,along witha variety of other comorbidities, through a multivariable linear regression model.

The following table summarizes the model, where the estimated linear coefficients (slopes) are in the column "Parameter Estimate", followed by the standard error associated with each parameter estimate and the resulting t-value (which is simply the parameter estimate divided by its standard error).The column labeled "Pr>|t|" is the correspondingp-value associated with the t-value.For example, if you reject the null hypothesis that the intercept equals zero, you would do so with over an 85% chance of incorrectly rejecting this hypothesis - and therefore you should conclude that the intercept is statistically no different than zero.

Predictor Variable	Parameter Estimate	Standard Error	tValue	Pr>|t|
Intercept	-0.01305	0.06941	-0.19	0.8510
Heroin	0.25738	0.04337	5.93	<.0001
HepC	0.11499	0.06466	1.78	0.0763
HepB	0.06106	0.09432	0.65	0.5179
Liver Disease	0.58833	0.12178	4.83	<.0001
Viral Load	5.347417E-7	9.786719E-8	5.46	<.0001
STI	-0.10648	0.04453	-2.39	0.0174
AGE	0.00253	0.00174	1.45	0.1478
SEX	-0.05454	0.03569	-1.53	0.1275

1. Based on the table above, would you conclude that heroin usesignificantly increasesmortality in this population, after controlling for the other variables? (yes/no)
2. What other variables besides heroin use are significant, with no more than a 5% chance of incorrectly rejecting the null hypothesis (=0.05)?
3. Are any variables "marginally" significant, where there is more than a 5% chance of incorrectly rejecting the null hypothesis, but no more than a 10% chance of doing so(=0.10)?Either answer as "no" or list any variables that are marginally significant.

8 points

QUESTION 25

1. The margin of error equals the standard error multiplied by a critical Z or t value.True or False?

True

False

2 points

QUESTION 26

1. If a test statistic has an associatedp-valueof0.0356, then we can reject H₀if our maximum accepted type 1 error rate is set at =0.01.True or False?

True

False

2 points

QUESTION 27

1. If a 95% confidence interval for the difference in two independent means is (2.1 to 4.5), this indicates that we should not reject the null hypothesis, concluding there is no significant difference in the means, with respect to an =0.05 hypothesis test.True or False?

True

False

2 points

QUESTION 28

1. If we design a study to have no more than a 10% chance of a type 2 error, then the statistical power of the study equals 90%.True or False?

True

False

2 points

QUESTION 29

1. The probability of rejecting the null hypothesis when it is actually true is called the "type 1 error rate". True or False?

True

False

2 points

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