Question

An agronomist is an expert in soil management and crop production. A certain state hires an agronomist to investigate whether there is a linear relationship between a wheat stalk’s height and the yield of wheat. The agronomist 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 agronomist tested the following hypotheses.

H0 : β1 = 0
Ha : β1 ≠ 0
The test yielded a p -value of 0.25. Which of the following is a correct conclusion about the claim?
A. The null hypothesis is rejected because 0.25 > 0.05. There is sufficient evidence to suggest that there is a linear relationship between a wheat stalk's height and its yield.
B The null hypothesis is not rejected because 0.25 > 0.05. There is sufficient evidence to suggest that there is a linear relationship between a wheat stalk's height and its yield.
С The null hypothesis is rejected because 0.25 > 0.05. There is not sufficient evidence to suggest that there is a linear relationship between a wheat stalk's height and its yield.
D The null hypothesis is not rejected because 0.25 > 0.05. There is not sufficient evidence to suggest that there is a linear relationship between a wheat stalk's height and its yield.
E The null hypothesis is accepted because 0.25 > 0.05. There is sufficient evidence to suggest that there is not a linear relationship between a wheat stalk's height and its yield.

Answer 1

D The null hypothesis is not rejected because 0.25 > 0.05. There is not sufficient evidence to suggest that there is a linear relationship between a wheat stalk's height and its yield.

Explanation:

Given the hypothesis :

H0 : β1 = 0

Ha : β1 ≠ 0

The Pvalue = 0.25 ; α = 0.05

Decision region :

Reject H0 ; if Pvalue < α

Comparing the Pvalue and α - value

0.25 > 0.05

Here, the Pvalue is > α ; hence, we fail to reject the Null, H0

Hence, there is no significant evidence to suggest that there is a linear relationship between what's stalk height and its yield.