401077 Introduction to Biostatistics Assessment 1 Answer
401077 Introduction to Biostatistics, Autumn 2019
Question 1 (6 marks)
- Hand grip strength (the variable “grip”) is a continuous variable as continuous variables are numeric variables that generally have an infinite number of values between any two values. Whereas, a categorical variable has a finite number of categories or groups which defines the set. So “grip” is continuous variable.
- As we can see that the number of overweight people is more than the obese and normal. Also, normal people are too less as compared to others.
- Interpretation of R: Talking about bmi summary statistics, Minimum and Maximum is 19.93 and 41.29 respectively and the centre is close to 28.37.
As the skewness is positive, the distribution of BMI is skewed right. Kurtosis value is greater than 3, so its tails are heavier compared to normal distribution, and central peak is lower and shorter.
Question 2 (6 marks)
Histogram of gripstrength by BMI calssification is displayed below.
It can be easily observed that Overweight persons has higher grip strength than normal and obese persons. Normal persons has lowest grip strength among these three groups.
b) Plot between BMI ands hand grip strength is displayed below in the figure.
The correlation between bmi and grip strength is -0.267 which means they are negatively correlated. But their strength is low. If grip is increased then bmi would decrease but slightly.
Question 3 (6 marks)
Table 1: Body Mass Classification by Occupation history
|Heavy Manual||8|| 37||20||65|
(Created by using ‘bmicat’ and ‘occ’ variables)
Table 2: Body Mass Classification distribution by occupation in percentage
|Heavy Manual||3.4334%|| 15.8798%|
We can see that the number of normal people with the occupation as heavy manual is the lowest and the number of overweight people with the occupation as other is the highest. Through the cross tabulation we can depict that if a person is selected at random then what is the probability of it being one of the cross-sectional data.
From the table produced in R-Commander, we can see that the probability of selecting one person at random would be an obese person with an occupation history of “heavy manual” is:
P = 20/233 (Total Number of observations)
P = 0.085
From the table produced in R-Commander, we can see that the probability of selecting one obese person at random would be with an occupation history of “heavy manual” is:
P = 20/76
P = 0.26
To determine the dependence and independence of 2 variables in a sample we use Chi-Square Test. In Chi-Square Test, Null Hypothesis is that the two variables are independent and Alternate Hypothesis is that the two variables are dependent. From the result, we can see that the p-value is above 0.05 so, we fail to reject the null hypothesis, which means the two variables are independent of each other.
Question 4 (6 marks)
Binomial model is used to determine the success of any given situation when the actions are repeated a number of times. Here we are selecting one person at random and the process is repeated 5 times in total so the binomial distribution model is best fit for such kind of scenarios.
Total number of obese people = 76
Total number of people = 233
Probability that 2 or 3 times it would be obese = 0.4827864
The mean in a binomial distribution is calculated by n*P where n is the number of trials and P is the probability of success. Here n=5 and probability of success is 0.5 so, mean would be 5*0.326 = 1.63. So, 1.63 is the mean which will be observed for all obese people if repetitions are repeated a number of times.
Question 5 (6 marks)
Mean is 32.19 and Standard Deviation is 3.94
Z-score for a participant who records a hand grip strength of 34 kilograms is 0.45.
Central limit theorem is basically used for normal distribution of data. We can see that the data given to us is almost normally distributed.
By using CLT,
32.83245, 31.93303 33.39408, 31.57391
The value of hand grip strength which is achieved or surpassed by only 5% of the grandparent carers is 25.70584.