Question

Consider the following set of random measurements, taken from a normally distributed population before and after a treatment was applied.

Before Treatment	[58.51, 58.34, 53.44, 52.27, 56.05, 54.32, 59.42, 52.84, 52.46]
After Treatment	[57.99, 64.05, 61.84, 57.04, 60.56, 61.79, 56.83, 62.54, 60.47]
Difference	[.52, -5.71, -8.40, -4.77, -4.51, -7.47, 2.59, -9.70, -8.01]

a) Determine the point estimate for the mean difference.

Round your response to at least 3 decimal places.

   

b) Calculate the standard error of the sample mean difference.

Round your response to at least 3 decimal places.

   

c) What is the margin of error for a 95% confidence interval for the mean difference?

Round your response to at least 3 decimal places.

    

Answer 1

a)

Point estimate for mean difference = -5.051

b)

std.dev = 4.148

std.errro = s/sqrt(n)
= 4.148/sqrt(9)
= 1.383

c)

sample mean, xbar = -5.051
sample standard deviation, s = 4.148
sample size, n = 9
degrees of freedom, df = n - 1 = 8

Given CI level is 95%, hence α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025, tc = t(α/2, df) = 2.306

ME = tc * s/sqrt(n)
ME = 2.306 * 4.148/sqrt(9)
ME = 3.188