Question

Find the estimated standard error for the sample mean for the following samples: (a) n= 9 with SS =1152

Answer 1

To find the estimated standard error for the sample mean, we need to divide the sample standard deviation by the square root of the sample size. However, we are given the sum of squares (SS), not the sample standard deviation, so we first need to calculate the sample variance. The formula for the sample variance is: s^2 = SS / (n - 1) where s^2 is the sample variance, SS is the sum of squares, and n is the sample size. Using the given values, we have: s^2 = 1152 / (9 - 1) = 144 Now we can find the estimated standard error: SE = s / sqrt(n) where SE is the estimated standard error, s is the sample standard deviation, and n is the sample size. Since s = sqrt(s^2), we have: SE = sqrt(s^2

Answer 2

To find the estimated standard error for the sample mean, we need to use the formula:

SE = s/√n

where s is the sample standard deviation and n is the sample size.

However, we are not given the sample standard deviation, but we are given the sum of squares (SS). We can use this to find the sample variance (s^2) and then take the square root to find the sample standard deviation.

For a sample size of n = 9, the degrees of freedom (df) are:

df = n - 1 = 9 - 1 = 8

Using the formula for the sample variance:

s^2 = SS/df = 1152/8 = 144

Taking the square root, we find the sample standard deviation:

s = √144 = 12

Now we can find the estimated standard error:

SE = s/√n = 12/√9 = 4

Therefore, the estimated standard error for the sample mean is 4.