Question

Consider the following results for independent random samples taken from two populations.  

Sample 1	Sample 2
n1= 10	n2 =  40
x1= 22.3	x2= 20.3
s1= 2.5	s2 = 4.1

a. What is the point estimate of the difference between the two population means (to 1 decimal)?  
  

b. What is the degrees of freedom for the  t distribution (round down)?  
  

c. At 95% confidence, what is the margin of error (to 1 decimal)?  
  

d. What is the 95% confidence interval for the difference between the two population means (to 1 decimal)?  

Answer 1

For the details of the given sample from two different population:

a) The point estimate would be difference between the mean as:

x1= 22.3

x2= 20.3

=X1-X2

=22.3-20.3

=2

b) Since the population are independent and different hence unequal variances are assumed so, the degree of freedom is calculated as:

df=25

c) At 95% the margin of error is calculated as:

=t_c​×SE

Where SE is the standard error and t_c is calculated using excel formula at calculated df as =T.INV.2T(0.05,25.438), which gives t_c as 2.058

Now the SE is calculated as:

and Margin of error as 1.022*2.058

=2.1

d. The confidence interval is now calculated as:

={-0.1, 4.1}