Question

Question In the theory of finance, a market for any asset or commodity is said to be efficient if items of identical quality and other attributes (such as risk, in the case of stocks) are sold at the same price. An oil industry analyst wants to test the hypothesis that the spot market for crude oil is efficient. He chooses the Rotterdam oil market and Arabian Light as the type of oil to be studied. A random sample of eight observations from each of four sources of the spot price (in U.S. dollars) of a barrel of oil during February is collected and displayed in the following table: 17.98 UK Mexico 17.80 18.01 18.00 17.75 18.00 18.20 17.77 18.00 18.01 17.99 18.01 18.10 18.12 17.90 18.20 UAE 18.10 17.92 18.01 17.88 18.30 18 22 18.56 18.10 Oman 18.05 18.01 17.94 18.23 18.20 18.00 17.84 18.11 Using this data, the analyst performed two tests with R and obtained the following printouts: ANOVA F-test of Sum Sq Mean Sq F value Pr(>F) source 0.1152 0.03839 1.469 Residuals 0.7315 0.02613 Kruskal-Wallis test Kruskal-Wallis rank sum test data: price and source Kruskal-Wallis chi-squared - 3.2635, df = . p-value = The df- and p-values are deliberately hidden on these printouts.

im really lost with this topic. i would really appreciate the detailed answer.

Answer 1

The assumptions of the Kruskal-Wallis test are:

Samples are random samples, or allocation to treatment group is random. The two samples are mutually independent. The measurement scale is at least ordinal, and the variable is continuous.

All the assumptions are met.

The hypothesis being tested is:

H₀: n₁ = n₂ = n₃ = n₄

H_a: At least one median rank is not equal

Decision rule: Reject Ho if the p-value < 0.05.

The p-value is 0.3528.

Since the p-value (0.3528) is greater than the significance level (0.05), we fail to reject the null hypothesis.

Therefore, we cannot conclude that the spot market for crude oil appears inefficient.