Question

the test yielded a t -value of 2.086 with a corresponding p -value of 0.05. which of the following is the correct interpretation of the p -value? responses if there is a linear relationship between the amount of mercury in a lake and the surface area of the lake, the probability of observing a test statistic as extreme as 2.086 or more extreme is 0.05. if there is a linear relationship between the amount of mercury in a lake and the surface area of the lake, the probability of observing a test statistic as extreme as 2.086 or more extreme is 0.05. if there is a linear relationship between the amount of mercury in a lake and the surface area of the lake, the probability of observing a test statistic of 2.086 is 0.05. if there is a linear relationship between the amount of mercury in a lake and the surface area of the lake, the probability of observing a test statistic of 2.086 is 0.05. if there is not a linear relationship between the amount of mercury in a lake and the surface area of the lake, the probability of observing a test statistic of 2.086 or greater is 0.05. if there is not a linear relationship between the amount of mercury in a lake and the surface area of the lake, the probability of observing a test statistic of 2.086 or greater is 0.05. if there is not a linear relationship between the amount of mercury in a lake and the surface area of the lake, the probability of observing a test statistic of 2.086 is 0.05. if there is not a linear relationship between the amount of mercury in a lake and the surface area of the lake, the probability of observing a test statistic of 2.086 is 0.05. if there is not a linear relationship between the amount of mercury in a lake and the surface area of the lake, the probability of observing a test statistic as extreme as 2.086 or more extreme is 0.05.

Answer 1

The correct interpretation of the p-value in this scenario is "if there is a linear relationship between the amount of mercury in a lake and the surface area of the lake, the probability of observing a test statistic as extreme as 2.086 or more extreme is 0.05." This means that if there is actually no linear relationship between the amount of mercury in a lake and the surface area of the lake, there is a 5% chance of obtaining a test statistic as extreme as 2.086 or more extreme purely by chance. Therefore, a p-value of 0.05 is commonly used as a threshold to reject the null hypothesis and conclude that there is evidence of a linear relationship between the two variables.

Explanation: