Question

A scientist claims that there is a linear relationship between a lake’s flow rate and its runoff factor. The scientist collected data and used the data to test the claim that there is a linear relationship at a significance level of α=0.05. The scientist tested the following hypotheses.

H₀ : β₁ = 0
Hₐ : β₁ ≠ 0

The scientist found a p-value of 0.02 for the test. Which of the following is a correct conclusion about the scientist's claim?

A. The null hypothesis is rejected since 0.02 <0.05. There is sufficient statistical evidence to suggest that there is a linear relationship between a lake's flow rate and runoff factor
B. The null hypothesis is not rejected since 0.02 < 0.05. There is sufficient evidence to suggest that there is a linear relationship between a lake's flow rate and runoff factor
C. The null hypothesis is rejected since 0.02 <0.05. There is not sufficient evidence to suggest that there is a linear relationship between a lake's flow rate and runoff factor
D. The null hypothesis is not rejected since 0.02 < 0.05. There is not sufficient Devidence to suggest that there is a linear relationship between a lake's flow rate and runoff factor.
E. The null hypothesis is accepted since 0.02 < 0.05. There is sufficient evidence to suggest that there is not a linear relationship between a lake's flow rate and runoff factor

Answer 1

The correct conclusion is to reject the null hypothesis since the p-value is less than the significance level; there is sufficient evidence for a linear relationship between a lake's flow rate and runoff factor. Option A is the correct answer.

Step-by-step explanation:

A scientist tested the claim that there is a linear relationship between a lake's flow rate and its runoff factor. This was done by setting up a hypothesis test, with the null hypothesis H₀: β₁ = 0 (which states that there is no linear relationship), against the alternative hypothesis Hᴇ: β₁ ≠ 0 (which states that there is a linear relationship).

The scientists found a p-value of 0.02 for the linear relationship test. When we compare this p-value with the significance level α = 0.05, and because the p-value is less than the significance level (0.02 < 0.05), we reject the null hypothesis.

This means there is sufficient statistical evidence at the 5 percent significance level to suggest that there is a significant linear relationship between a lake's flow rate and its runoff factor. Therefore, the correct conclusion is Option A: The null hypothesis is rejected since 0.02 < 0.05. There is sufficient statistical evidence to suggest that there is a linear relationship between a lake's flow rate and runoff factor.