Posted: June 25th, 2022

MPH5041 Introductory Biostatistics


Question 1: Identify the following variables from the table.

Question 2: Compile the following table with appropriate summary statistics for each variable.

Discuss the relationship between dyslipidemia and HbA1c (diastolic BP), insulin status, and patients’ ages.

Question 3: Determine the relationship between dyslipidemia and each of these variables: BMI, duration of diabetes and occupation type.

Discuss the variables by presenting them on a graph.

Question 4: The following questions will show detailed calculations. Most marks will be assigned for correct calculations.

(a) A battery’s life expectancy is usually distributed with a 40 hour mean and a 1.2 hour standard deviation.

Find out how likely it is that a randomly chosen battery will last longer than 42 hours.

(b) In a hospital, all employees who were hired in the last five years are usually distributed by their ages.

This curve shows 95% of the ages to be between 24.6 and 37.3 years.

Find the average age and standard deviation.

(c) The scores of medical tests follow a normal distribution, with a mean score of 460 and a standard error of 100.

What is the likelihood that a given class of 41 students will score above 589.93 if they all take the test?

Question 5: Take into account that the distribution of the systolic pressure in the population can be positively skewed.

How will the distribution of large samples of the mean systolic bloodpressure in the sample be affected?

Question 6: Briefly explain the differences between:

A prospective cohort study and a randomized clinical trial (RCT).

Study of case-control and historical cohorts.

Prospective cohort study, and historical cohort study




Identification Number


Age in years

Age Group


1: 40-49 years; 2: 40-49 years; 3: 50-59 years; 4: >= 60 Years.


1: Male; 2 Female

Type of occupation


1: Sedentary worker. 2: Moderate worker. 3: Heavy physical worker.

Physical Activity Level


0: Sufficient PA

1 Insufficient PA

Weight in Kg

Height in meters

BMI (in Kg/m2)


Diastolic BP


Diabetes duration

Diabetes Group Duration


1: 5 years; 2:5 -10 years; 3:>=10 years

HbA1c Group


0: 7 Years; 1: >=7 Years

Use insulin


0: No, 1: Yes

Durability of Insulin (years).

Total Cholesterol




0: Normal, 1: Low



Ratio TC_HDL




Dyslipidemia (%, median &IQR or mean and SD)



Insulin status



Age group

40 Years

40-49 years

50-59 Years

>= 60 Years

Clustered bar charts are the best way to show the relationship between categorical variables.

This chart is the best to illustrate the relationship between categorical variable.

Figure 3.1 clearly shows that dyslipdaemia occurs in obese people more than in normal people.

Figure 3.1: Relationship of BMI Group and Dyslipdaemia

Figure 3.2 again shows that dyslipdaemia is linked to age.

Figure 3.3 illustrates the relationship between dyslipdaemia and age.

This shows that dyslipdaemia can be severe in sedentary workers, but is very rare in heavy-duty physical workers.

Figure 3.2: Relationship between diabetes and dyslipdaemia

Figure 3.3: Relationship of occupation type and dyslipdaemia

Let X be the battery’s lifetime.

Normally, the life expectancy of a battery can be divided into two parts.

The standard deviation is 1.2 hours, while the mean life is 40 hours.

The probability that a randomly chosen bulb will last more than 42 hours is P (X = 42).

Let X be the ages of all employees who were hired in the past 5 years at a hospital.

These ages are distributed as normal.

The (24.6, 37.5) gives the 95% confidence interval for the ages.

Because the data are normally distributed, you can say that the difference in the confidence interval can easily be divided into four equal parts to calculate the standard deviation.

The standard deviation is ((37.4-24.6) / 4 = 3.2).

The mean can be found by approaching the left side of the distribution with two standard deviations.

The mean can be calculated as ((37.4 + (2 * 3.2),) = 31

Let X be the score of a medical exam.

Normal distribution of scores for a medical test.

The average score is 460, and the standard deviation 100.

The probability that a given class will score more than 589.93 is therefore P (X >589.93).

Positively, the distribution of systolic bloodpressure in the population is skewed.

The distribution of sampling will therefore be normal.

This is based on the central limit theorem.

According to this theorem, if there are many random samples taken from a population, then the sample means for each one will equal the population mean u or the standard deviation s.

The population will have the same distribution as the sample.

If the sample is large, regardless of how big the population, the distribution will be normal.

This case shows that the population is normally distributed.

The theorem states that the sampling distribution for blood pressure is normally distributed because it contains an innumerable amount of random samples.

1.A random clinical trial is a study in which participants are randomly assigned to different treatment groups.

Researchers and participants are not permitted to pick which group a participant will be placed in.

The random selection will be made.

The procedure can make the different groups comparable and allow for objective comparisons of the treatments received in each group.

The best treatment will not be known until the trial begins.

The patient has complete freedom to choose whether or not he wishes to take part in the random trial.

This is a random clinical trial.

Prospective cohort studies are when a study is done over a prolonged period of time with a group of people who have a lot in common and one that is different (eg, smokers and non-smokers female nurses). This allows for comparison of their outcomes (eg., lung carcinoma).

2.Case Control is a comparison of two groups of patients.

The one group has a specific disease and the other does not.

It can also indicate the risk of being exposed to the disease and the relationship between them.

A retrospective cohort study, on the other hand is a type of research study in which the medical records of participants that are similar in many ways but different in one characteristic are compared to determine the outcome of interest.

This data is available at all times and does not require experiments.

3. Participants of interest in both retrospective and prospective cohort studies are the same.

All of them share a common characteristic, but differ in one.

Prospective cohort studies are different because they use the same samples and monitor them over time.

The collection of data can be time-consuming.

Retrospective studies are done based on medical history data.

In prospective studies, the sample is chosen and the data are collected by monitoring them. However, retrospective studies use the data obtained first and the sample selected based on the accepted data.

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