Solution Found!
(In some of the exercises that follow, we must
Chapter 8, Problem 9E(choose chapter or problem)
When a stream is turbid, it is not completely clear due to suspended solids in the water. The higher the turbidity, the less clear is the water. A stream was studied on 26 days, half during dry weather (say, observations of X) and the other half immediately after a significant rainfall (say, observations of Y). Assume that the distributions of X and Y are \(N(\mu_X , \sigma^2)\) and \(N(\mu_Y , \sigma^2)\), respectively. The following turbidities were recorded in units of NTUs (nephelometric turbidity units):
x: 2.9 14.9 1.0 12.6 9.4 7.6 3.6
3.1 2.7 4.8 3.4 7.1 7.2
y: 7.8 4.2 2.4 12.9 17.3 10.4 5.9
4.9 5.1 8.4 10.8 23.4 9.7
(a) Test the null hypothesis \(H_0: \mu_X = \mu_Y\) against \(H_1: \mu_X < \mu_Y\). Give bounds for the p-value and state your conclusion.
(b) Draw box-and-whisker diagrams on the same graph. Does this figure confirm your answer?
Questions & Answers
QUESTION:
When a stream is turbid, it is not completely clear due to suspended solids in the water. The higher the turbidity, the less clear is the water. A stream was studied on 26 days, half during dry weather (say, observations of X) and the other half immediately after a significant rainfall (say, observations of Y). Assume that the distributions of X and Y are \(N(\mu_X , \sigma^2)\) and \(N(\mu_Y , \sigma^2)\), respectively. The following turbidities were recorded in units of NTUs (nephelometric turbidity units):
x: 2.9 14.9 1.0 12.6 9.4 7.6 3.6
3.1 2.7 4.8 3.4 7.1 7.2
y: 7.8 4.2 2.4 12.9 17.3 10.4 5.9
4.9 5.1 8.4 10.8 23.4 9.7
(a) Test the null hypothesis \(H_0: \mu_X = \mu_Y\) against \(H_1: \mu_X < \mu_Y\). Give bounds for the p-value and state your conclusion.
(b) Draw box-and-whisker diagrams on the same graph. Does this figure confirm your answer?
ANSWER:Step 1 of 5
Given:
A stream was studied on 26 days, half during dry weather (say, observations of X) and the other half immediately after a significant rainfall (say, observations of Y).
The number of observations of X is n=13.
The number of observations of Y is m=13.