Question

A dependent random sample from two normally distributed populations gives the results shown below. Complete parts a and b below.

n=19

d =28.7

sd=3.8

a. Find the 90% confidence interval for the difference between the means of the two populations.

The 90​% confident interval is from a lower limit of _?_ to an upper limit of _?_.

b. Find the margin of error for a 90% confidence interval for the difference between the means of the two populations.

The margin of ME = ?

Answer 1

a)

sample size ,    n =    19
Level of Significance ,    α =    0.10

Degree of freedom, DF=   n - 1 =    18
t-critical value =    t α/2,df =    1.7341
      
std dev of difference , Sd =        3.8000
      
std error , SE =    Sd / √n =    0.8718
margin of error, E =    t*SE =    1.5117
      
mean of difference ,    D̅ =   28.7000
confidence interval is       
Interval Lower Limit=   D̅ - E =   27.1883
Interval Upper Limit=   D̅ + E =   30.2117

The 90​% confident interval is from a lower limit of 27.2 to an upper limit of 30.2

b)

.margin of error = 1.5 [ as calculated above]