# Biostatistics Practice Problems

The following are some biostatistics practice questions that you can use to enhance your understanding of the course material. Practice answering these questions and they will give you an excellent and practical biostatistics tutor solutions.

## BASIC DESCRIPTION OF DATA, GATHERING, ANALYSIS, AND PRESENTATION

1. What do we call a characteristic that is different between individuals_____________? Such a characteristic may be numerical (e.g., heartbeats per minute), and it may be categorical such as the neighborhood in which you live as distinguished from another.
1. Sample
2. Mean
3. Variable
4. Data
2. What do we call a study where subjects are given treatments randomly?
1. Randomized Experiment
2. Poll
3. Participants Bias
4. Sample Variable
3. On which basis can we make cause and effect conclusions?
1. Sample
2. Data
3. Randomized Experiment
4. Randomized Experiment
4. In statistics, what do we call the fact that researchers test different theories in a single study?
1. Multiple Variables
2. False Positive
3. Clinical Study
4. Multiple Hypothesis
5. What is similar to a bar graph, and is it used for all data variables?
1. Axis
2. Stem & Leaf
3. Histogram
4. Boxplot

## DESCRIPTIONS OF DATA AND ITS NORMAL DISTRIBUTION

1. A random survey of 4016 girls aged 9 showed that their average height was 137 cm with a 5 cm standard deviation. Using a histogram, the researchers concluded that the heights of study participants were within the normal distribution. Using this information, answer the following questions.
1. The heights of three of the participating girls were as follows 140 cm, 160 cm, 123 cm. The list below consists of descriptions that fit each of the three girls. Match each of the girls with a description and justify your answer. Please note that you can use a description more than once.
• Unusually tall
• Within the average range
• Unusually short
2. Two of the participants were 153 cm tall. How far above average were they by SDs?
3. One participant was 2 SDs below the mean height. How tall was she?
4. If one of the survey participants’ height was within 3.2 SDs of the mean height. Find out the shortest and the tallest she could have been.
2. In a survey, researchers measured the blood sugar level of 1500 participants, and they calculated the standard deviation. A second survey followed the same population, but the second one had three times more participants than the first one (4500). Considering this information indicate which of the following statements is true.
1. The standard deviation of the new sample will be more significant than the first, but it is impossible to tell how much bigger.
2. The second sample’s standard deviation will be smaller than the first by about a third of the size.
3. The new sample’s standard deviation will be bigger than the previous survey by about three times.
4. All the statements are false; there is no reason for the SD to change since participants are from the same pool.

## SAMPLING DISTRIBUTIONS AND CONFIDENCE INTERVALS

1. You undertake a study to determine how many teenagers between 17 and 19 have had a Sexually Transmitted Infection in the past two years. You get a sample of 400 girls, out of which 250 accept your invitation to participate. On the 250 participants, a 90% confidence interval for the participants who had contracted STI within the research period was .11 to .22. In the statements below, find out which is true on which proportion of the 150 who failed to participate had contracted an STI within the period of interest.
1. The proportion can’t be in the interval of .11-.22
2. The proportion is sure to be within the proportion of .11-.22
3. The proportion will be exactly as it was with participants, .11-.22 with 90% confidence.
2. If you randomly took 10000 samples from a state all discharge data sets where every sample has 200 discharges and calculated the mean for each sample. You then create a histogram with the 10000 means. Pick the statement below that would best describe the resulting histogram.
1. It looks like a uniform distribution.
2. It appears more or less like a normal distribution as the Central Limit Theorem applies to the large samples involved.
3. It is skewed to the left
4. It is skewed to the right
5. It appears more or less like a normal distribution as the Central Limit Theorem applies because the survey involves many samples.

## HYPOTHESIS TESTING

1. A study is intended to find out whether Omega 3 fatty acids improve memory in senior citizens. Towards this end, researchers found seniors aged between 70 and 80, and they randomly selected some of the participants to take Omega 3 and the rest to take a placebo for six months. Researchers gave the participant a test after the treatment period, and the seniors who had taken Omega 3 posted better results than those who had taken the placebo. Eighty of them took the supplement, and their mean test score and standard deviation were 31 and 6.1, respectively. Eighty-one seniors took the placebo, and their mean test score and standard deviation were 23 and 6.3, respectively. Using this information:
1. What is the best statistical test to use when comparing the mean test scores of the supplement group and the placebo group?
2. Is this study limited as a way of drawing conclusions on the effectiveness of Omega 3’s ability to enhance cognitive ability in seniors? If your answer is yes, list all the ways in which it is limited.
3. Calculate a 90% confidence interval for the average difference in test scores between the two groups.
4. What conclusion would you as a biostatistician draw from this survey?
2. Researchers involved two sets of expectant mothers in determining the effect of a prescription drug on fetuses. One group of mothers took the prescription drug in question, and the other group didn’t, and both groups were picked randomly. Babies were examined once they were born, and researchers found a consistent pattern of different head sizes between the children whose mothers took the drug and those whose mothers didn’t (p = .03). From this information, select the accurate conclusions in the list below.
1. Taking the prescription drug by a pregnant mother causes their child’s head to shrink.
2. The mean difference in the sizes of heads of the children born by the two sets of mothers is clinically significant.
3. Taking the prescription drug causes fetuses’ heads to increase.
4. The null hypothesis is 3% likely to be true.
5. None of the above.
3. In a study, 300 patients with hypertension were randomly divided into 155 and 145 participants. They put the first group under diet while the second was placed under an exercise regimen, both meant to manage the condition while still on medication. Their blood pressure was measured at the beginning of the study and three months after the programs. Researchers noted some changes between the two. Which of the following statistical procedures would be best placed to determine if the mean blood pressure reduction was significant?
1. 2 Sample unpaired
2. Paired t-test
3. Fisher’s exact test
4. None of the above

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