Question

Identifying \({H_0}\) and \({H_1}\) . In Exercises 5–8, do the following:

a. Express the original claim in symbolic form.

b. Identify the null and alternative hypotheses.

Pulse Rates Claim: The standard deviation of pulse rates of adult males is more than 11 bpm. For the random sample of 153 adult males in Data Set 1 “Body Data” in Appendix B, the pulse rates have a standard deviation of 11.3 bpm.

Short answer

a.The original claim in symbolic form is written in the following manner:

\(\sigma > 11\;{\rm{bpm}}\)

b. The null hypothesis and the alternative hypothesis are as follows:

\({H_0}:\sigma = 11\)

\({H_1}:\sigma > 11\)

Step-by-step solution

Given information

For a sample of 153 adult males, the pulse rate hasa standard deviation,which is equal to 11.3 bpm.

Original claim

a.

It is claimed that the standard deviation of the pulse rate of adult males is more than 11 bpm.

Symbolically, the claim would be \(\sigma > 11\;{\rm{bpm}}\), where\(\sigma \) is the standard deviation of the pulse rate of all adult males.

Hypotheses

b.

Null hypothesis: The standard deviation of the pulse rate of adult males is equal to 11 bpm.

\({H_0}:\sigma = 11\)

Alternative hypothesis: The standard deviation of the pulse rate of adult males is more than 11 bpm.

\({H_1}:\sigma > 11\)