Final answer:
The p-value of 0.026 is less than the significance level of 0.05, leading us to reject the null hypothesis and conclude there is a significant correlation between oil prices and stock prices in the given sample.
Step-by-step explanation:
The correlation found between the average price of oil and average stock price for this sample of 13 securities is 0.71. To test the significance of this correlation at alpha = 0.05, we'll use a two-tailed test. The calculation of the p-value would involve using a statistical software or calculator that can perform the appropriate correlation significance test (e.g., LinRegTTest or equivalent). However, commonly for correlation tests, the t-distribution is used, and the degrees of freedom would be n - 2 (where n is the sample size).
In this scenario, the calculated p-value is 0.026. When comparing the p-value to the significance level alpha, we see that 0.026 is less than 0.05. This means we reject the null hypothesis, indicating there is significant evidence of a linear relationship between the average price of oil and average stock prices for the year.
Therefore, the conclusion would be that there is a statistically significant correlation between the variables in question, and this relationship is not occurring by chance at the 5 percent significance level.