An energy analyst wants to test if U.S. oil production is random over time. The analyst has monthly production values for the two years. The analyst finds 12 months are above the median, 12 months are below the median, six runs are below the median, and five runs are above the median. Using the p-value approach and α = 0.01, the appropriate conclusion is ________.
A) do not reject the null hypothesis; we can conclude oil production is not random
B) reject the null hypothesis; we can conclude oil production is not random
C) reject the null hypothesis; we cannot conclude oil production is not random
D) do not reject the null hypothesis; we cannot conclude oil production is not random

Question

Quizplus · Accepted Answer

To test if U.S. oil production is random over time, we need to use the runs test. The null hypothesis is that the observations are random over time. We can use the runs test to determine if the number of runs in the data set is consistent with what we would expect if the null hypothesis were true.

Here, the analyst found 12 months above the median and 12 months below the median. The runs below the median count is 6 and the runs above the median count is 5. The p-value approach assumes a large sample size, which is not the case here, so we will use the normal approximation to the binomial distribution instead.

Using the runs test, we calculate the test statistic as follows:
Z = (R-mu_R) / sigma_R
where R is the number of runs, mu_R is the expected number of runs, and sigma_R is the standard deviation of the number of runs.

The expected number of runs is given by:
mu_R = [(2n-1) / 3]
where n is the sample size.

The standard deviation of the number of runs is given by:
sigma_R = [(16n-29) / 90]^.5

Plugging in the values, we get:
mu_R = [(2*24-1)/3] = 15.67
sigma_R = [(16*24-29)/90]^.5 = 2.14

The observed number of runs is:
R = 6 + 5 = 11

Using the normal approximation to the binomial distribution, we have:
Z = (11 - 15.67) / 2.14 = -2.18

Looking up the p-value for a standard normal distribution with α = 0.01, we find that the p-value is approximately 0.015. Since the p-value is greater than α, we do not have sufficient evidence to reject the null hypothesis. Therefore, the appropriate conclusion is that we cannot conclude that U.S. oil production is not random over time. The answer is D, do not reject the null hypothesis; we cannot conclude oil production is not random.

An Energy Analyst Wants to Test If U