Question

In an investigation of pregnancy-induced hypertension, one group of women with this disorder was treated with low-dose aspirin, and a second group was given a placebo. A sample consisting of 23 women who received aspirin has mean arterial blood pressure 111 mm Hg and standard deviation 8 mm Hg; a sample of 24 women who were given the placebo has mean blood pressure 109mm Hg and standard deviation 8 mm Hg. Suppose that the required assumptions to make inference for μ1 − μ2 are satisfied. Obtain any p-values or critical values using R.

2.1 Explain why this problem has to be analyzed as an independent samples situation.

2.2 What are the assumptions required in order to be able to make inference for μ1 − μ2 ?

2.3 For each of the 6 numbers given in the statement of the problem (on page 280), write the symbol used to represent each quantity and its corresponding value. For example, write X bar = 8, etc.

2.4 Obtain a 98% confidence interval for the difference of means between both groups (group 1 minus group 2). Treat the women that received aspirin as group 1. Provide answer with at least 2 decimals.

2.5 Use your interval in the previous part to make a conclusion regarding testing whether there is a difference in means or not. Use α = 0.02. Justify your conclusion. Page 2

2.6 For the test in the previous part, will the power of the test be higher when δ = μ1 − μ2 = 2 or when δ = 1? Why?

Note: δ is Greek letter delta. There is no need to actually calculate the power at any of those 2 values.

2.7 Suppose that the researchers think that arterial blood pressure will either be the same for both groups or it will be lower for those who took low-dose aspirin. Use μ1 to represent the mean arterial blood pressure for those who were treated with low-dose aspirin. Conduct a relevant test of hypothesis with a level of significance of 0.05. Go through each of the four steps and label them. Provide p-value with at least 2 decimals.

Answer 1