help me work out the problem to calculate the difference means distribution parameters n(1)=25, n(2)=36 s(1)square=50, s(2) square=72, M(1)=100,M(2)=105
To calculate the difference between means distribution parameters, we need to follow these steps:
Step 1: Calculate the pooled standard deviation (s_pooled).
The pooled standard deviation is a weighted average of the individual standard deviations, based on their sample sizes. It is calculated using the following formula:
s_pooled = sqrt(((n1 - 1) * s1^2 + (n2 - 1) * s2^2) / (n1 + n2 - 2))
Given that n1 = 25, n2 = 36, s1^2 = 50, and s2^2 = 72, we can substitute these values into the formula:
s_pooled = sqrt(((25 - 1) * 50 + (36 - 1) * 72) / (25 + 36 - 2))
Simplifying this expression:
s_pooled = sqrt((24 * 50 + 35 * 72) / 59)
s_pooled = sqrt((1200 + 2520) / 59)
s_pooled = sqrt(3720 / 59)
s_pooled ≈ sqrt(63.05)
s_pooled ≈ 7.95
Step 2: Calculate the standard error (SE).
The standard error (SE) represents the standard deviation of the sampling distribution of the difference between means. It is calculated using the following formula:
SE = s_pooled * sqrt((1/n1) + (1/n2))
Substituting the values we already have:
SE = 7.95 * sqrt((1/25) + (1/36))
Simplifying this expression:
SE = 7.95 * sqrt(0.04 + 0.02778)
SE = 7.95 * sqrt(0.06778)
SE ≈ 7.95 * 0.26
SE ≈ 2.07
Step 3: Calculate the difference between means.
The difference between means is calculated by subtracting the two means, M1 and M2:
Difference between means = M1 - M2
Given that M1 = 100 and M2 = 105:
Difference between means = 100 - 105
Difference between means = -5
Therefore, the difference between means is -5.