## Question

Attached excel file named PROTHROM for this question

Refer to the prothrombin time data on 1000 infants (PROTHROM). Select a simple random sample of size 16 from each of these populations and conduct an appropriate hypothesis test to determine whether one should conclude that the two populations differ with respect to mean prothrombin time.

Let α = 0.05 What assumptions are necessary for the validity of the test?

MUST INCLUDE discussion of the data, objectives of the analysis summary and conclusions, as well as supporting numeric and graphic software results in R (attach R file)

Question 2

Attached excel file named HEMOGLOB for this question

Refer to the hemoglobin data on 500 children with iron deficiency anemia and 500 apparently healthy children (HEMOGLOB). Select a simple random sample of size 16 from population A and an independent simple random sample of size 16 from population B. Does your sample data provide sufficient evidence to indicate that the two populations differ with respect to mean Hb value?

Let α = 0.05 What assumptions are necessary for the validity of the test?

MUST INCLUDE discussion of the data, objectives of the analysis summary and conclusions, as well as supporting numeric and graphic software results in R (attach R file)

## Solution Preview

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Question 1Discussion of the data:

The data for prothrombin time for 1000 infants was collected and there were two groups i.e. FULLSUB and PRESUB. Since, the data is divided into 1:1 for each group which means there are 500 observations for each group. To perform the task we have to select a random sample of 16 observations. This will be done by using seed (1), so that we will get the same observations every time we run the code.

Objectives of the analysis:

Our objective is to determine from the data if the two populations differ with respect to mean prothrombin time or not.

For our objective we will be defining the following hypothesis

H0: There is no significant difference in the prothrombin time between the groups i.e. µ1= µ2

Ha: There is a significant difference in the prothrombin time between the groups i.e. µ1≠ µ2

Where µ1 is mean of TIME_FULL and µ2 is mean of TIME_PRE

The test will be conducted at 5% level of significance.

Since, the number of observation is less than 30 we will check the normality of the data for each group to assess if the data is normally distributed or not....

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Solution.R and Solution.docx.