Question

Independent samples from two regions of the same area gave the following chemical measurements (ppm). Assume the population distributions are approximately normal. Region 1: 438, 306, 402, 1155, 1075, 500, 340 Region 2: 778, 387, 816, 767, 479, 710, 389, 826 Find a 90% confidence interval for the difference between the means.

(a) What is the point estimate?

(b) What is the margin of error?

(c) What is the lower limit?

(d) What is the upper limit?

(e) What is the confidence interval?

Answer 1

The sample sizes are small, . Since the population standard deviations are not known, we use T-test.

a)Here, the sample means are . The sample standard deviations are

The point estimate of the difference in means is

b) The margin of error is

With , The margin of error is

e)The 90% confidence interval for difference in means is

c) The lower limit is

d)The upper limit is  

.