Question

You want to calculate a 95% confidence interval (CI) for the difference between the means of two variables. The variables are from populations with normal distributions and those distributions have the same standard deviation (σ). To make your estimate you will take the same number of samples from each population, calculate the mean for each sample, calculate the difference between those sample means, and then add or subtract the term that defines the CI. If you want the width of the CI to be less than 2×σ, what is the minimum number of samples you should take from each sample?

Answer 1

. If you want the width of the CI to be less than 2×σ, what is the minimum number of samples you should take from each sample

we have to find minimum number of sample is given as

here value of Z is 1.96 for 95% confidence interval

Where margin of error is the half the width of confidence interval

here half the width will be

approximate 4 samples are required

Confidence interval for difference of means is given as by below formula

because it has been given that

S1=S2=S

n1=n2=n

so

Where value of Z is 1.96 for 95% confidence interval