Question

1. A clinical trial is held to compare a newly discovered antihypertensive drug to an existing medication. The study involves a total of 200 hypertension patients. Patients are enrolled and randomized to receive either the experimental new drug or the existing medication. The data shown below are data collected of their systolic blood pressure readings measured at the end of the study after 6 months on the assigned treatments. (Sp = 17.23)

	New drug (n=100)	Existing drug (n=100)
Mean systolic blood pressure	120.2	131.4

Test if there is a significant difference in mean systolic blood pressures between groups using α=0.05.

1. We reject Ho
2. We accept Ho
3. We do not reject Ho
4. Insufficient information

Answer 1

To Test :-

H0 :-  $\mu_{1} = \mu_{2}$

H1 :-  $\mu_{1} \neq \mu_{2}$

Test Statistic :-

$t = (\bar{X_{1}} - \bar{X_{2}}) / S_{p}\sqrt{ ( 1 / n1) + (1 / n2)}$

$t = ( 120.2 - 131.4) / 17.23 \sqrt{ ( 1 / 100) + (1 / 100 )}$

$t = -4.5964$

Test Criteria :-
Reject null hypothesis if $| t | > t_{\alpha /2, n1 + n2 - 2}$
$t_{\alpha /2, n1 + n1 - 2} = t_{ 0.05 /2, 100 + 100 - 2} = 1.972$
$| t | > t_{\alpha /2, n1 + n2 - 2} = 4.5964 > 1.972$
Result :- Reject Null Hypothesis

Option A is correct.