Question

A ten randomly selected oil wells in a large field produced 21, 19, 20, 22, 24, 21, 19, 22, 22, and 20 barrels of crude oil per day. Is this enough evidence to conclude that the oil wells are not producing an average of 22.5 barrels of crude oil per day? Test at 0.01 level of significance. (t-test)

Answer 1

No, 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.

Step-by-step explanation:

To determine whether the oil wells are producing an average of 22.5 barrels of crude oil per day, we can perform a t-test. The null hypothesis is that the average is 22.5 barrels and the alternative hypothesis is that the average is different from 22.5 barrels. We can calculate the sample mean, standard deviation, and perform the t-test using the given data.

First, calculate the sample mean: (21 + 19 + 20 + 22 + 24 + 21 + 19 + 22 + 22 + 20) / 10 = 210 / 10 = 21 barrels.

Next, calculate the sample standard deviation: sqrt(((21-21)^2 + (19-21)^2 + (20-21)^2 + (22-21)^2 + (24-21)^2 + (21-21)^2 + (19-21)^2 + (22-21)^2 + (22-21)^2 + (20-21)^2) / (10-1)) = sqrt((0 + 4 + 1 + 1 + 9 + 0 + 4 + 1 + 1 + 1) / 9) = sqrt(22/9) = sqrt(2.44) ≈ 1.56 barrels.

Using a t-table or calculator, we can find the critical value for a 0.01 level of significance and degrees of freedom equal to the sample size minus 1 (10-1 = 9). The critical value is approximately 3.25 (two-tailed test).

Now, calculate the t-statistic: (21 - 22.5) / (1.56 / sqrt(10)) ≈ -2.39.

Since the absolute value of the t-statistic is less than the critical value, we fail to reject the null hypothesis. This means that 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.