Question

Assume that a sample is used to estimate a population mean μμ. Find the margin of error M.E. that corresponds to a sample of size 13 with a mean of 64.2 and a standard deviation of 9.3 at a confidence level of 95%.

Report ME accurate to one decimal place because the sample statistics are presented with this accuracy.
M.E. =

Answer should be obtained without any preliminary rounding. However, the critical value may be rounded to 3 decimal places.

Answer 1

Solution :

Given that,

= 64.2

s =9.3

n = Degrees of freedom = df = n - 1 = 13- 1 = 12

a ) At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

  / 2= 0.05 / 2 = 0.025

t /2,df = t0.025,12 = 2.179 ( using student t table)

Margin of error = E = t/2,df * (s /n)

= 2.179* ( 9.3/ 13)

= 5.6