Question

Hypotheses Identify the null and alternative hypotheses for using the sample data from Exercise 8 in testing the claim that for differences between right-arm systolic blood pressure amounts and left-arm systolic blood pressure amounts, those differences are from a population with a mean equal to 0.

Short answer

The hypotheses are stated below:

$\begin{array}{l}{H}_o:{\mu }_d=0\mathrm{m}\mathrm{m}\mathrm{H}\mathrm{g}\\ H_1:{\mu }_d\ne 0\mathrm{m}\mathrm{m}\mathrm{H}\mathrm{g}\end{array}$

Here,${\mu }_d$ is the difference betweentwo true mean blood pressure measurements (left- and right-hand measurements in mm Hg) of the population.

Step-by-step solution

Given information

Refer to Exercise 8 for the study of systolic blood pressure measurements in mm Hg.

Explain the hypotheses

Hypotheses are always expressed in pairs, one being the null and the other alternative. The null expresses the supposition, which includes no change, while the alternative expresses the supposition for change in results.

Thus, the null hypothesis is always expressed with an equal to sign (greater than or equal to as well as less than or equal to).

Identify the hypotheses for the claim

It is required to test the claim using the reference exercise 8; that the difference in the true mean measurements of the blood pressure in left and right arm for populations is 0.

Let${\mu }_{L,}{\mu }_R$be the true mean measurements of the blood pressureleft and right arm, respectively, for a population of subjects.

As the data consists of paired samples (each observation in two samples is from one subject), it is a case of a hypothesis test for dependent samples.

Define${\mu }_d={\mu }_L-{\mu }_R$as the difference in two mean measures.

Thus, the hypotheses are formulated as per the claim.

$\begin{array}{l}{H}_o:{\mu }_d=0\mathrm{m}\mathrm{m}\mathrm{H}\mathrm{g}\\ H_1:{\mu }_d\ne 0\mathrm{m}\mathrm{m}\mathrm{H}\mathrm{g}\end{array}$