Question

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.

Answer 1

Answer:

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.

( the null is rejected and alternate is accepted)

Step-by-step explanation:

Here the critical value is t≥ t∝/2(n-2) = ± 2.086

The significance level is ∝= 0.05 and  the p- value is also 0.05

Which indicates that there is no correlation between the dependent and the independent variable.

If the p - value is less than 0.05 the null hypothesis is rejected.

There is a 5% chance that the  hypothesis is true.

So the null hypothesis should be rejected.

Given these options

a) if------as 2.086 or more extreme is 0.05

2.086 or 0.05 is the same in this case one cannot be more extreme.

c)  of 2.086 or greater is 0.05.

b). If there is a linear relationship ------.

This is the alternate hypothesis.

0.05 is not greater than 2.086 in the given question

d)  If there is not a linear relationship between the amount of mercury in-----.

This is the claim which is formulated as null  hypothesis.

e) if----  2.086 or more extreme is 0.05.

0.05 is the same as 2.086

At p- value 0.05 we reject the null hypothesis and accept the alternate hypothesis