Solution Found!
Answer: Crude oil biodegradation. Refer to the Journal of
Chapter 7, Problem 60E(choose chapter or problem)
Problem 60E
Crude oil biodegradation. Refer to the Journal of Petroleum Geology (April 2010) study of the environmental factors associated with biodegradation in crude oil reservoirs, Exercise 6.37 (p. 319). Recall that 16 water specimens were randomly selected from various locations in a reservoir on the floor of a mine and that the amount of dioxide (milligrams/liter)—a measure of biodegradation—as well as presence of oil were determined for each specimen. These data are reproduced in the accompanying table.
a. Conduct a test to determine if the true mean amount of dioxide present in water specimens that contained oil was less than 3 milligrams/liter. Use = .10.
b. Repeat part a for water specimens that did not contain oil.
Questions & Answers
QUESTION:
Problem 60E
Crude oil biodegradation. Refer to the Journal of Petroleum Geology (April 2010) study of the environmental factors associated with biodegradation in crude oil reservoirs, Exercise 6.37 (p. 319). Recall that 16 water specimens were randomly selected from various locations in a reservoir on the floor of a mine and that the amount of dioxide (milligrams/liter)—a measure of biodegradation—as well as presence of oil were determined for each specimen. These data are reproduced in the accompanying table.
a. Conduct a test to determine if the true mean amount of dioxide present in water specimens that contained oil was less than 3 milligrams/liter. Use = .10.
b. Repeat part a for water specimens that did not contain oil.
ANSWER:
Step 1 of 2
(a)
16 water specimens were randomly selected from various locations in a reservoir on the floor of a mine and that the amount of dioxide (milligrams/liter).
These data are represented in the table.
Dioxide Amount |
Crude Oil Present |
3.3 |
No |
0.5 |
Yes |
1.3 |
Yes |
0.4 |
Yes |
0.1 |
No |
4.0 |
No |
0.3 |
No |
0.2 |
Yes |
2.4 |
No |
2.4 |
No |
1.4 |
No |
0.5 |
Yes |
0.2 |
Yes |
4.0 |
No |
4.0 |
No |
4.0 |
No |
We are asked a test to determine if the true mean amount of dioxide present in water specimens that contained oil was less than Use
Using MINITAB, the descriptive statistics are:
Step to create the descriptive statistics in Minitab:
- On the opening of Minitab, you will get session handler and worksheet like Excel worksheet.
- Enter the data into the worksheet (in this case dioxide amount and crude oil present).
- After entering the data go to a menu called Stat in menu panel and under that select Basic Statistics option.
- In the drop down menu of Basic Statistics option, select Display Descriptive Statistics.
- You will get a window of Display Descriptive Statistics and list of variables that you have entered in a worksheet.
- In “variables” space, select dioxide amount and in “by variables (optional)” space, select crude oil present.
- After clicking ok you will get the summary of mean, median etc.
To determine if the mean amount of dioxide present in water specimens that contain oil is less than we test the following hypothesis,
We can write,
Since the sample size is very less, hence we will use the test statistic.
A lower or left tailed test about a population mean is,
Rejection rule for a lower tail test: The Critical Value Approach from the figure 1
……..(1)
Hence the test statistic for hypothesis tests about a population mean when is known,
………(2)
We know hence we can rewrite the equation (2),
[condition when crude oil present from the descriptive statistics]
………(3)
The rejection region requires
in the lower tail of the
with
From the table III, Appendix D, the value of
…….(4)
From equation (3) and (4) we can see that the observed value of the test statistic falls in the rejection region.
Since,
Hence is rejected and there is sufficient evidence to indicate the true mean of dioxide amount present in water specimens that contain oil is less than
at