Based on the given data, there is not enough evidence to conclude that the oil wells are not producing an average of 22.5 barrels of crude oil per day at the 0.01 level of significance.
How to test the claim
To determine whether the oil wells are not producing an average of 22.5 barrels of crude oil per day, conduct a hypothesis test using the given data.
Let's define the null hypothesis (H0) and the alternative hypothesis (Ha):
H0: The average production of the oil wells is 22.5 barrels per day.
Ha: The average production of the oil wells is not 22.5 barrels per day.
We will use a t-test since we have a small sample size (n = 10) and the population standard deviation is unknown.
Here are the steps to perform the hypothesis test:
Calculate the sample mean and the sample standard deviation (s) for the given data.
Sample mean = (21 + 19 + 20 + 22 + 24 + 21 + 19 + 22 + 22 + 20) / 10 = 20.0 barrels per day
Sample standard deviation (s) =
≈ 1.837 barrels per day
Calculate the t-statistic using the formula:
t = (
- μ) / (s /
(n))
Where μ is the hypothesized population mean (22.5), s is the sample standard deviation, and n is the sample size.
t = (20.0 - 22.5) / (1.837 /
(10)) ≈ -2.72
Determine the critical value for a two-tailed test at the 0.01 level of significance. Since the sample size is small, we will use a t-distribution and degrees of freedom equal to (n - 1) = 9.
The critical value for a two-tailed test with α = 0.01 and df = 9 is approximately ±3.250.
Compare the absolute value of the t-statistic with the critical value to make a decision.
|t| = |-2.72| < |3.250|
Since the absolute value of the t-statistic is less than the critical value, we fail to reject the null hypothesis.
Therefore, based on the given data, there is not enough evidence to conclude that the oil wells are not producing an average of 22.5 barrels of crude oil per day at the 0.01 level of significance.