# 8. Anexperiment to determine the efficacy of a drug for reducing high blood pressureis performed using four subjects in the following way: two of the subjects arechosen at random for the control group and two for the treatment group. Duringthe course of treatment with the drug, the blood pressure of each of the subjects inthe treatment group is measured for ten consecutive days as is the blood pressureof each of the subjects in the control group.a. In order to test whether the treatment has an effect, do you think it is appropriateto use the two-sample t test withb. Do you think i20?it is appropriate touse the Mann-Whitney test withn20

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Asked Apr 23, 2019
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Step 1

a.

Two sample t test:

Two sample independent t test is a parametric test used to check for differences between means of two sets of observations, usually  samples are taken from two separate populations.

The required assumptions to use two sample t test:

• The samples must be independent and drawn randomly from the populations.
• Observations in each sample must be independent.
• Either the sample size must be greater than 30 or the populations must be normally distributed.

Here, it is given that two subjects are chosen at random for the control group and 2 subjects are chosen at random for treatment group. The blood pressure of both the group patients is measured for 10 consecutive days.

Here, a patient from one day to the next day might not be independent observation.

In general, the blood pressure of a patient for the consecutive days might not be independent. Further more, the sample sizes are not greater than 30 and also the populations are not said to be normally distributed.

Therefore, the two sample t test is not appropriate for the given situation.

Step 2

b.

Mann-Whitney U Test:

Mann-Whitney U test is a non-parametric test used to check for differences between two sets of observations, usually samples are taken from two separate populations.

In this procedure, the sample observations from the two populations are first combined and given a combined rank.

Suppose the number of observations in sample 1 is n1 and the number of observations in sample 2 is n2.

Let R1 be the sum of ranks of the sample 1 observations and R2 be the sum of ranks of the sample 2 observations.

The required assumptions to use two sample t test:

• Independ...

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