Mathematics, 24.04.2021 04:20 DakotaOliver

A scientist is interested in whether there is a linear relationship between the amount of mercury in a lake and the surface area of the lake. The scientist collected data on 22 lakes of a similar type selected at random and used the data to test the claim that there is a linear relationship. The following hypotheses were used to test the claim. H0:β=0

Ha:β≠0

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?

a. 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
b. 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.
c. 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.
d. 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.
e. 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.

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