Question

Given two independent random samples with the following results

: n1=16

x‾1=92

s1=24   

n2=12

x‾2=130

s2=31

Use this data to find the 80% confidence interval for the true difference between the population means. Assume that the population variances are equal and that the two populations are normally distributed.

Step 1 of 3: Find the point estimate that should be used in constructing the confidence interval.

Step 2 of 3: Find the margin of error to be used in constructing the confidence interval. Round your answer to six decimal places.

Step 3 of 3: Construct the 80% confidence interval. Round your answers to the nearest whole number.

Answer 1

1)

Point estimate = (1 - ​​​​​2) = 92 - 130 = -38

2)

Pooled standard deviation Sp = Sqrt [ (n1-1) S²1 + (n2-1) S²2 / n1 + n2 -2 ]

=sqrt [ 15 * 24² + 11*31² / 16 + 12 - 2 ]

= 27.182432

t critical value at 0.20 level with 26 df = 1.315

Margin of error E = t *Sp * sqrt (1 / n1 + 1 / n2)

= 1.315 * 27.182432 *Sqrt ( 1 / 16 + 1 / 12)

E = 13.650308

c)

80% Confidence interval is

(1 - ​​​​​2) - E < 1 - 2 < (1 - ​​​​​2) + E

-38 - 13.650308 <  1 - 2 < -38 + 13.650308

-52 <  1 - 2 < -24

80% CI is ( -52 , -24)