Question

*** do not solve the question

*** i have uploaded the data to matlab, show how do i code to run ttest for this question (provide exact codes)  

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stion 18 marks In a study concerned with the effects of smoking on blood pressure, the smoking status (Yes- 1, No -0) and systolic blood pressure (mmHg) were recorded for 500 randomly selected people. The purpose of the following analysis is to determine whether the systolic blood pressure of smokers is significantly different from that of non-smokers. The data are available on MyUni in the file BP.csv (a) Explain briefly why the data should be treated as two independent samples rather than paired (b) Use MATLAB to perform a two-independent sample t-test. State the value of the test statistic, the reference distribution with appropriate degrees of freedom, and the P-value. Do you reject or retain the null hypothesis at the 5% level of significance? Make sure to include the code you used in MATLAB to run the test, along with the output (do NOT include any code used to import/write out data) (c) Determine if the assumptions of the test are met. Include any plots you produce to support your comments, and comment on the validity of the P-value you obtained in Part (b) 2 F 500x2 table SystolicBP S oke 133 115 140 132 133 138 133 67 138 130 103 137

Answer 1

a)

Let me first quote an example of paired sample and two independent samples

Suppose a manufacturing company has manufactured two drugs namely drug A and drug B and the company is interested to know which drug is best by administering the drug to rats, this can be done in two ways

i) One is by taking one group of rats and administering them with drug A and observing the result. Then for a short span of time these rats are not administered with any drug (this short span of time which we call the "wash-out" period (So that the effect of drug A vanishes completely)). After the wash-out period the same group of rats are administered with drug B and the effects of the drugs are observed. In this scenario the two drugs are administered on the same group of rats. In this case the the data collected on the rats when administering the drugs is called as paired sample

ii) Another way is by taking 2 different groups of rats and administering drug A to the first group of rats and administering drug B to the second group of rats and then observing the effect of the drug A and drug B on group 1 and group 2 respectively. In this case we have two independent groups of rats and the data collected on these two groups in called as two independent samples

In the above data of smokers and non smokers the two groups should be treated as two independent samples rather than paired, because smokers and non smokers are two independent categories.

b)

The data for this question is not provided, however the procedure for the test is as follows.

First do the F test (where Ho : Variance of systolic blood pressure of the two groups are equal)

CASE 1 : If the p-value of F test is greater that 0.05 then we accept the null hypothesis (Variance of systolic blood pressure of the two groups are equal) and we do the two independent sample t-test using the following MATLAB code

[h,p] = ttest2(x,y,'Vartype','unequal')

Where x and y are the systolic blood pressure of group A and group B respectively.

The output will have h and p values

If h = 1, this indicates the rejection of the null hypothesis at the Alpha significance level.

If h = 0, this indicates a failure to reject the null hypothesis at the Alpha significance level.

If the p-value of this test is greater that 0.05 then we accept the null hypothesis (The mean systolic blood pressure of the smokers and non smokers are the same groups are equal)

CASE 2 : If the p-value of F test is lesser that 0.05 then we reject the null hypothesis (Variance of systolic blood pressure of the two groups are not equal) and we do the two independent sample t-test using the following MATLAB code

[h,p] = ttest2(x,y)

Where x and y are the systolic blood pressure of group A and group B respectively.

The output will have h and p values

If h = 1, this indicates the rejection of the null hypothesis at the Alpha significance level.

If h = 0, this indicates a failure to reject the null hypothesis at the Alpha significance level.

If the p value of this test is greater that 0.05 then we accept the null hypothesis (The mean systolic blood pressure of the smokers and non smokers are the same groups are equal)

c)

One of the assumptions is regarding the variance which I have explained in the previous subdivision

Another assumption is that the data follows normality using the Q- Q plot. Or ks test for normality can be done.

The two samples are drawn from two independent samples