Answer:
Step-by-step explanation:
Hello!
The objective of the research is to compare the newly designed drug to reduce blood pressure with the standard drug to test if the new one is more effective.
Two randomly selected groups of subjects where determined, one took the standard drug (1- Control) and the second one took the new drug (2-New)
1. Control
X₁: Reduction of the blood pressure of a subject that took the standard drug.
n₁= 23
X[bar]= 18.52
S= 7.15
2. New
X₂: Reduction of the blood pressure of a subject that took the newly designed drug.
n₂= 21
X[bar]₂= 23.48
S₂= 8.01
The parameter of study is the difference between the two population means (no order is specified, I'll use New-Standard) μ₂ - μ₁
Assuming both variables have a normal distribution, there are two options to estimate the difference between the two means using a 95% CI.
1) The population variances are unknown and equal:
[(X[bar]₂-X[bar]₁)±[tex]t_{n_1+n_2-2;1-\alpha /2}[/tex]*([tex]Sa\sqrt{\frac{1}{n_1} +\frac{1}{n_2} }[/tex])]
[tex]t_{n_1+n_2-2;1-\alpha /2}= t_{23+21-2;1-0.025}= t_{42;0.975}= 2.018[/tex]
[tex]Sa=\sqrt{\frac{(n_1-1)*S_1^2+(n_2-1)S_2^2}{n_1+n_2-2} } = \sqrt{\frac{22*7.15^2+20*8.01^2}{42} }= 7.57[/tex]
[23.48-18.52]±2.018*([tex]7.57*\sqrt{\frac{1}{21} +\frac{1}{23} }[/tex])]
[0.349; 9.571]
2) The population variables are unknown and different:
Welche's approximation:
[(X[bar]₂-X[bar]₁)±[tex]t_{Dfw;1-\alpha /2}[/tex]*( [tex]\sqrt{\frac{S_1^2}{n_1} +\frac{S_2^2}{n_2} }[/tex])]
[tex]Df_{w}= \frac{(\frac{S_1^2}{n_1} +\frac{S^2_2}{n_2} )^2}{\frac{(\frac{S_1^2}{n_1} )^2}{n_1-1}+ \frac{(\frac{S_2^2}{n_2} )^2}{n_2-1} } = \frac{(\frac{7.15^2}{23} +\frac{8.01^2_2}{21} )^2}{\frac{(\frac{7.15^2}{21} )^2}{20}+ \frac{(\frac{8.01^2}{23} )^2}{22} } = 42.85= 42[/tex]
[tex]t_{Df_w;1-\alpha /2}= t_{42; 0.975}= 2.018[/tex]
[(23.48-18.52)±2.018[tex]\sqrt{\frac{7.15^2}{23} +\frac{8.01^2}{21} }[/tex]]
[0.324; 9.596]
I hope this helps!
