Question

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

Sample 1	Sample 2
n 1 = 40	n 2 = 30
x 1 = 13.1	x 2 = 11.1
σ 1 = 2.3	σ 2 = 3.4

1. What is the point estimate of the difference between the two population means? (to 1 decimal)
2. Provide a 90% confidence interval for the difference between the two population means (to 2 decimals). Use z-table.
   ( ,  )
3. Provide a 95% confidence interval for the difference between the two population means (to 2 decimals). Use z-table. If your answer is negative, enter minus (-) sign.
   ( ,  )

Answer 1

Solution: Here the given information are

sample 1 sample 2

n1=40 n2=30

=13.1   =11.1

=2.3 =3.4

a) The point estimate of the difference of the population means is the difference of the sample means:

- = 13.1 - 11.1 = 2.0

b) 90% confidence interval is calculated as follows.

For confidence level 1-=0.90, determine = =,

=1-0.1/2 = 1-0.05 =0.95 -------(0.9500 find in the z table)

=1.645

The endpoints of the confidence interval for are :

(- )   *

(13.1-11.1) 1.645*

2 1.645*0.7194

(0.8166, 3.1834)

The 90% confidence interval for is  0.82 < < 3.18

c) 95% confidence interval is calculated as follows.

For confidence level 1-=0.95, determine = =,

= 1- 0.05/2 = 1-0.025 = 0.975--------------(0.9750 find in the z table)

= 1.96

The endpoints of the confidence interval for are :

(- )   *

(13.1-11.1) 1.96*

2 1.96*0.7194

( 0.5900, 3.4100)

The 95% confidence interval for is 0.59 < < 3.41