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: ; 438 1013 1127 737 491 840 306 402 1155 1075 500 340
Region II: ; 778 464 563 610 827 894 476 394 824 387 816 767 479 710 389 826

Required:
Find a 90% confidence interval.

The 90% confidence interval for the difference between means is (-161.18, 205.18).

Step-by-step explanation:

Sample mean and standard deviation for Region I:

Sample mean and standard deviation for Region II:

Now, we have to calculate a 90% confidence level for the difference of means.

The degrees of freedom are:

The critical value for 25 degrees of freedom and a confidence level of 90% is t=1.708

The difference between sample means is Md=22.

The estimated standard error of the difference between means is computed using the formula:

The margin of error (MOE) can be calculated as:

Then, the lower and upper bounds of the confidence interval are:

The 90% confidence interval for the difference between means is (-161.18, 205.18).

the formula of a slope:

from a table we have

substitute:

the slope of f(x) is -1.

the graph of funcfion g(x) is a horizontal line. the slope of a horizontal line is equal 0. therefore the slope of g(x) is 0.

-1 < 0