Question

Multiple Choice Select the best answer for Exercises 23-28. Exercises 23-28 refer to the following setting. To see if students with longer feet tend to be taller, a random sample of $25$students was selected from a large high school. For each student, $x=footlength$and $y=height$were recorded. We checked that the conditions for inference about the slope of the population regression line are met. Here is a portion of the computer output from a least-squares regression analysis using these data:

Is there convincing evidence that height increases as footlength increases? to answer this question, test the hypothesis

a.$\mathrm{H}0:\beta 1=0H_0:{\beta }_1=0$versus$H_{\alpha }:{\beta }_1\>0.H_{\alpha }:{\beta }_1>0$

b.$\mathrm{H}0:\beta 1=0H_0:{\beta }_1=0$versus$H_{\alpha }:{\beta }_1<H_{\alpha }:{\beta }_1\&lt;0$

c$\mathrm{H}0:\beta 1=0H_0:{\beta }_1=0$versus$H_{\alpha }:{\beta }_1\ne 0.H_{\alpha }:{\beta }_1\ne 0$

d$H_0:{\beta }_1\&gt;0H_0:{\beta }_1>0$versus$H_{\alpha }:{\beta }_1=0.H_{\alpha }:{\beta }_1=0$

e.$\mathrm{H}0:\beta 1=0H_0:{\beta }_1=0$versus$H_{\alpha }:{\beta }_1\&gt;1.H_{\alpha }:{\beta }_1>1$

Short answer

The correct option is option (a)

$H_0:{\beta }_1=0H_0:{\beta }_1=0versus{H}_{\alpha }:{\beta }_1>0$

Step-by-step solution

Given Information

Given in the question that

we have to determine the correct option.

Explanation

The slope is positive (y grows as x increases), according to the claim.

The null hypothesis statement, also known as the alternative hypothesis statement, asserts that the slope is zero. The alternative hypothesis statement is the polar opposite of the null hypothesis if the mention claim is the null hypothesis.

therefore the correct option is option (a)