Question

Consider two medications, studied in a laboratory and, which are supposed to reduce the response time to a certain stimulus. The investigator is inclined to believe that the response times, after administering both drugs, follow a normal distribution with equal variances of 50. As part of the evaluation of the two drugs, medication A applies to 25 individuals and medication B it is administered to another 10. The researcher is interested in knowing between what values 95 percent central would be of all the differences between the means of the samples, if both drugs were equally effective and if the experiment was repeated a large number of times using these sample sizes.

Answer 1

Solution :-

Here we need 95% confidence interval for difference of means.

Standard Deviation(σ_A⁼σ_B⁼σ)=Sqrt(50)=7.07

Given, n_A=25, n_B=10

at 95% confidence interval, critical value of z = 1.96.

So , required confidence interval is:-

(11-i2) -critical . σ -+ n2

=(x̅_A-x̅_B) ± 1.96*7.07(SQRT(1/25+1/10))

=(x̅_A-x̅_B) ±5.185

as both the drugs were equally effective so here (x̅_A-x̅_B) =0

Hence,

Required Confidence Interval =(-5.185,5.185) ....ans