Question

Use the t-distribution to find a confidence interval for a difference in means μ1-μ2 given the relevant sample results. Give the best estimate for μ1-μ2, the margin of error, and the confidence interval. Assume the results come from random samples from populations that are approximately normally distributed.

A 90% confidence interval for μ1-μ2 using the sample results x¯1=81.1, s1=10.3, n1=35 and x¯2=67.1, s2=7.9, n2=20

Enter the exact answer for the best estimate and round your answers for the margin of error and the confidence interval to two decimal places.

Answer 1

= 81.1, s1 = 10.3, n1 = 35

= 67.1, s2 = 7.9, n2 = 20

c = 90% , = 0.10

1)
Best point estimate =   = 81.1 - 67.1 = 14

Best point estimate = 14

2)

formula for margin of error is

where,

df = n1 + n2 - 2 = 35 + 20 2 = 53

1.674

Sp = 9.509528

= 4.462176451

Margin of error = 4.46

14 - 4.462176451 , 14 + 4.462176451

Confidence interval = ( 9.54 , 18.46 )