Biostatistics

Q 6

Question 1

For a matched pair t-test of H0: µd = 0 vs. Ha: µd ? 0, a sample with n = 51 has the mean and standard deviation of the differences 1.8 and 3.9 respectively. What is the value of the test statistic?

Answer
a) 0.46
b) 3.30
c) 3.80
d) 4.05

Question 2

Eleven patients were weighed before and after a diet which was designed to help patients reduce weight. Eight of these patients did lose weight but three patients had a weight increase.To test whether the diet is successful (i.e., post weight is lower than pre-weight) using post weight-pre-weight, state the appropriate null and alternative hypotheses.

Answer
a) H0: µd=0, HA: µd<0
b) H0: µd=0, HA: µd>0
c) H0: µd=0, HA: µd ? 0

Question 3

One of the assumptions underlying the paired-samples t-test is that difference scores are ________ distributed in the population.

Answer
a) Unfairly
b) Widely
c) Normally
d) All of the above
Question 4

The effectiveness of a diet designed to lower serum cholesterol is to be evaluated by measuring the cholesterol of eight patients identified as being at risk for cardiovascular disease before and after being on the diet for 16 weeks. Use the data below to construct a 95% confidence interval for the mean difference. Hint: sd = 10.068 Please show your work.

Patient Before Diet After Diet
1 213 199
2 252 241
3 195 197
4 222 220
5 267 248
6 216 224
7 209 209
8 255 237

Answer
Question 5

A clinical trial is planned to compare an experimental medication designed to lower blood pressure to a placebo. Before starting the trial, a pilot study is conducted involving 7 participants. The objective of the study is to assess how systolic blood pressure changes over time untreated. Systolic blood pressures are measured at baseline and again 4 weeks later Is there a statistically significant difference in blood pressures over time? Run the test at a 5% level of significance.

Baseline 120 145 130 160 152 143 126
4 Weeks 122 142 135 158 155 140 130

Write out the appropriate null hypothesis and the alternative hypothesis

Question 6

For #5, calculate and report the appropriate test statistic. Please show your work.

Question 7

For #5, decide to either fail to reject null hypothesis or reject null hypothesis in favor of the alternative hypothesis and describe the result and the statistical conclusion in an understandable way.

Question 8

A clinical trial is conducted comparing a new pain reliever for arthritis to a placebo. Participants are randomly assigned to receive the new treatment or a placebo and the outcome is pain relief within 30 minutes. The data are shown below.
Pain Relief No Pain Relief
New Medication 44 76
Placebo 21 99
Is there a significant difference in the proportions of patients reporting pain relief? Run the test at a 5% level of significance.
Write out the appropriate null hypothesis and the alternative hypothesis.
Question 9

For question #8, calculate and report the appropriate test statistic. Please show your work.

Question 10

For question #8, decide to either fail to reject null hypothesis or reject null hypothesis in favor of the alternative hypothesis and describe the result and the statistical conclusion in an understandable way.

Question 11

A hypertension trial is mounted and 12 participants are randomly assigned to receive either a new treatment or a placebo. Each participant takes the assigned medication and their systolic blood pressure (SBP) is recorded after 6 months on the assigned treatment. The data are as follows.

Placebo New Treatment
134 114
143 117
148 121
142 124
150 122
160 128

Is there a difference in mean SBP between treatments? Use alpha=.05.
Write out the appropriate null hypothesis and the alternative hypothesis (hint: one-sided or two-sided?).

Question 12

For #11, calculate and report the appropriate test statistic. Please show your work.

Question 13

For #11, decide to either fail to reject null hypothesis or reject null hypothesis in favor of the alternative hypothesis and describe the result and the statistical conclusion in an understandable way.
Answer

Question 14

605 survivors of a heart attack, were randomly assigned follow either (1) a diet close to the “prudent diet step 1” of the American Heart Association or (2) a Mediterranean-type diet consisting of more bread and cereals, more fresh fruit and vegetables, more grains, more fish, fewer delicatessen food, less meat. Over four years, researchers collected information on number of deaths from cardiovascular causes e.g., heart attack and strokes. The data are shown in the table below:
Diet Deaths Alive Total
AHA 24 279 303
Mediterranean 14 288 302
Total 38 567 605

Is there a significant difference in the number of patients who die of cardiovascular disease across the two diet plans? Run the test at a 5% level of significance.
Write out the appropriate null hypothesis and the alternative hypothesis .

Answer

Question 15

For #14, calculate and report the appropriate test statistic. Please show your work.

Question 16

For #14, decide to either fail to reject null hypothesis or reject null hypothesis in favor of the alternative hypothesis and describe the result and the statistical conclusion in an understandable way.