Question

Independent random samples from two regions in the same area gave the following chemical measurements (ppm). Assume the population distributions of the chemical are mound-shaped and symmetric for these two regions. Region I: ; 981 726 686 496 657 627 815 504 950 605 570 520 Region II: ; 1024 830 526 502 539 373 888 685 868 1093 1132 792 1081 722 1092 844 Let be the population mean and be the population standard deviation for . Let be the population mean and be the population standard deviation for . Determine and examine the 90% confidence interval for . Does the interval consist of numbers that are all positive? all negative? or different signs? At the 90% level of confidence, is one region more interesting that the other from a geochemical perspective?

Select one:

a. The interval contains only positive numbers. We can say at the required confidence level that one region is more interesting than the other.

b. The interval contains both positive and negative numbers. We cannot say at the required confidence level that one region is more interesting than the other.

c. The interval contains both positive and negative numbers. We can say at the required confidence level that one region is more interesting than the other. Incorrect

d. The interval contains only negative numbers. We cannot say at the required confidence level that one region is more interesting than the other.

e. The interval contains only positive numbers. We cannot say at the required confidence level that one region is more interesting than the other.

Answer 1

Ans:

	Region 1	Region 2
1	981	1024
2	726	830
3	686	526
4	496	502
5	657	539
6	627	373
7	815	888
8	504	685
9	950	868
10	605	1093
11	570	1132
12	520	792
13		1081
14		722
15		1092
16		844
	678.08	811.94
	163.85	239.04

df=12-1=11

critical t value=tinv(0.1,11)=1.796

90% confidence interval for difference in means

=(678.08-811.94)+/-1.796*sqrt((163.85^2/12)+(239.04^2/16))

=-133.85+/-136.88

=(-270.73, 3.03)

Option b is correct.

The interval contains both positive and negative numbers. We cannot say at the required confidence level that one region is more interesting than the other.