Given the following information about a hypothesis test of the difference between two means based on independent random samples, what is the standard deviation of the difference between the two means? Assume that the samples are obtained from normally distributed populations having equal variances.
H0: μA ≤ μB, and H1: μA > μB 1 = 12, 2 = 9, s1= 5, s2 = 3, n1 =13, n2 =10.
Standard deviation (standard error) of the difference between two means =
√[(s1^2 / n1) + (s2^2 / n2)]
I'll let you take it from here.
To calculate the standard deviation of the difference between the two means, we can use the formula:
Standard Deviation of the Difference = sqrt( (s1^2/n1) + (s2^2/n2) )
Where:
- s1 and s2 are the sample standard deviations of the two samples
- n1 and n2 are the sample sizes of the two samples
From the information given:
s1 = 5
s2 = 3
n1 = 13
n2 = 10
Plugging in these values into the formula:
Standard Deviation of the Difference = sqrt( (5^2/13) + (3^2/10) )
= sqrt( (25/13) + (9/10) )
= sqrt( (325/130) + (117/130) )
= sqrt( (442/130) )
≈ 3.167
Therefore, the standard deviation of the difference between the two means is approximately 3.167.