Question

A t-test is used to compare the means of one variable for two groups of cases. As an example, a practical application would be to find out the effect of a new drug on blood pressure. Patients with high blood pressure are randomly assigned into two groups, a placebo group and a treatment group. The placebo group would receive conventional treatment while the treatment group would receive a new drug that is expected to lower blood pressure. After treatment for a couple of months, the two sample t-test is used to compare the average blood pressure of the two groups. Below are the results. Determine the alpha value. Complete all five steps for hypothesis test. Conduct and interpret a 99% confidence interval. Sample size for placebo group 120, Sample size for treatment group 120 sample mean for placebo group 127 sample mean for treatment group 125 sample standard deviation for placebo group 4.5 sample standard deviation for treatment group 5.5

Answer 1

Hypothesis test-

We have two perform two sample t-test.

Suppose, random variables X and Y denote blood pressure for placebo and treatment groups respectively.

We have to test for null hypothesis

against the alternative hypothesis

Our test statistic is given by

Here,

Degrees of freedom

Level of significance

Corresponding    [Using R-code '1-pt(3.08301,238)+pt(-3.08301,238)']

We reject our null hypothesis if .

Here we observe that .

So, we reject our null hypothesis.

Hence, based on the given information we can conclude that blood pressure of placebo and treatment groups are not same.

99% confidence interval-

For degrees of freedom 238 we have,

So, 99% confidence interval is given by (-1.684486, 1.684486).

It implies that if blood pressure in placebo and treatment groups are not significantly different, then if we take 100 different pairs of samples, on average in 99 times the difference of average blood pressure of two groups will lie in the interval (-1.684486, 1.684486).