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 a = 0.05. The scientist tested the following hypotheses.

Hₒ: 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 C 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 evidence 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

A linear relationship exists between lake's flow rate and runoff factor and the correct option is 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.

The p-value (0.02) is less than the significance level (0.05), which means that there is a statistically significant difference between the observed data and what would be expected if there was no linear relationship between the lake's flow rate and runoff factor.

In other words, the data provides enough evidence to reject the null hypothesis (ᵦ₁ = 0) and conclude that there is a linear relationship between the two variables.

Therefore, the scientist's claim that there is a linear relationship between a lake's flow rate and runoff factor is supported by the statistical analysis.