Question

A medical researcher wants to determine if an experimental drug to control the Covid 19 Virus has any effect on the motor skills scores of human subjects. She randomly assigns patients to 1 of 2 groups. Nine hundred subjects in group 1 (the experimental group) are given an oral dose of the drug prior to testing (mean = 9.78, standard deviation = 4.05); 1000 subjects in group 2 (control group) receive a placebo (mean = 15.10, standard deviation = 4.28). Test the null hypothesis (at 95% confidence) that there is no difference between the population means of the drug group & the placebo group. What do you conclude?

Answer 1

since sample size is large we can use z distribution.

null hypothesis: Ho:μ1-μ2			=	0
Alternate hypothesis: Ha:μ1-μ2			≠	0
for 0.05 level with two tail test , critical z=				1.960
Decision rule : reject Ho if absolute value of test statistic |z|>1.96
	Population 1		Population 2
x1            =	9.78	x2            =	15.10
n1           =	900	n2           =	1000
σ1           =	4.05	σ2           =	4.28

std error σx1-x2=√(σ21/n1+σ22/n2)=sqrt(4.05^2/900+4.28^2/1000)=			0.191
test stat z =(x1-x2-Δo)/σx1-x2     =(9.78-15.10)/0.191 =			-27.83

since test statistic falls in rejection region we reject null hypothesis

we have sufficient evidence to conclude that there is  difference between the population means of the drug group & the placebo group