Answer to Question #249331 in Statistics and Probability for boo

Question

A research group wishes to conduct a randomized trial to compare a new medication to a medication
they consider standard care. One hundred patients with hypertension are enrolled and randomized
to one of the two comparison treatments. After taking the assigned medication for 6 weeks, their
systolic blood pressure (SBP) is measured. Summary statistics are given here. Use the data to test
if there is a significant difference in systolic blood pressures between medication groups assuming
equality of the variances. Run the appropriate test at a 5% level of significance.
Treatment Number of Patients Mean SBP Standard Deviation
New 50 130 12
Standard 50 135 10

Answer 1

$n_1= 50 \\ \bar{x_1} = 130 \\ s_1 = 12 \\ n_2 = 50 \\ \bar{x_2} = 135 \\ s_2 = 10 \\ H_0: \mu_1=\mu_2 \\ H_1: \mu_1 ≠ \mu_2$

Test-statistic:

$t = \frac{\bar{x_1} - \bar{x_2}}{\sqrt{s^2_{p} \times (\frac{1}{n_1} + \frac{1}{n_2})}} \\ s^2_{p} = \frac{(n_1-1) \times s^2_1 + (n_2-1) \times s^2_2}{n_1+n_2-2} \\ = \frac{(50-1) \times 12^2 + (50-1) \times 10^2}{50+50-2} \\ = 122 \\ t = \frac{130-135}{\sqrt{122 \times (\frac{1}{50} + \frac{1}{50})}} \\ = -2.263$

P-value

By using t distribution p-value table at α= 0.05, t = -2.263, $df = n_1+n_2- 2 = 98$

p-value = 0.0258

p-value < level of significance

We have to reject H₀ at α= 0.05.

There is sufficient evidence to conclude that the significant difference in systolic blood pressures between medication groups assuming equality of the variances.