Cholesterol Case Study

Question 1 (Difference Between Means): Is there a significant difference between drug type in mean relative-change* of Cholesterol from screening to follow up?
It will be important to investigate the effect of drug since the company whose data is being analyzed conducted the study to understand the effect of two comparable cholesterol lowering drugs. Other important aspect was to examine other factors like weight and BMI to understand their influence on cholesterol level. Hence, cholesterol being a common variable, will allow to further investigate the relation to other variables. This would allow us to combine our analysis for each question and reach to a conclusion about the effects on subjects due to Drug A and Drug B; and other factors

As upper fence value is greater than maximum value there are no outliers between the maximum value and upper fence. To further investigate the outliers, normality plots can be drawn. For drug B there seem to be no outliers. This can be confirmed using normality plots.
(II) Statistical Inferences and Graphical representation of data:
Normality Plot:
Step 1 Arrange the data in ascending order.
Step 2 Compute f_i=(i-0.375)/(n+0.25),* where i is the index and n is the number of observations. The expected proportion of observations less than or equal to the ith data value is fi .
Step 3 Find the z-score corresponding to fi from Table V.
Step 4 Plot the observed values on the horizontal axis and the corresponding expected z-scores on the vertical

An error of greater than 5% would make the data and statistical inferences less reliable.
Test statistic When making inferences about the difference between two means, a t-statistic is calculated
The requirements for the t test are The samples are obtained using simple random sampling or through a completely randomized experiment with two levels of treatment. In this case we can assume that random sampling was used to assign the drug treatment The samples are independent. The populations from which the samples are drawn are normally distributed or the sample sizes are large (>30). In this case population B appears to be normally distributed however population A may be skewed to the right For each sample, the sample size is no more than 5% of the population size.

Classical Approach
(t=(x ̅_1-x ̅_2 )-(μ_1-μ_2))/√(□(〖s1〗^2/n1)+□(〖s2〗^2/n2))

Since we assume the population means to be equal, 1=2 and therefore the t statistic is
(0.077-0.017) / (((0.121)2 /22) + ((0.145)2