Question

claim: the standard deviation of pulse rates of adult males is less than 10 bpm. for a random sample of 167 adult males, the pulse rates have a standard deviation of 8.7 bpm. complete parts (a) and (b) below.
a. express the original claim in symbolic form.
σ < 10 bpm
(type an integer or a decimal. do not round.)
b. identify the null and alternative hypotheses.
h₀: ▢ ▢ ▢ bpm
h₁: ▢ ▢ ▢ bpm
(type integers or decimals. do not round.)

Explanation:

Step1: Understand the claim

The claim is about the standard deviation of pulse rates of adult males being less than 10 bpm. In statistics, the symbol for population standard deviation is \(\sigma\). So the original claim in symbolic form is \(\sigma< 10\) bpm.

Step2: Determine the null and alternative hypotheses

The null hypothesis \(H_0\) is a statement of equality. Since the claim is \(\sigma < 10\), the null hypothesis will be the opposite (to start with the assumption of no difference or the status - quo). So \(H_0:\sigma = 10\) bpm.
The alternative hypothesis \(H_1\) is the claim we are trying to find evidence for. So \(H_1:\sigma<10\) bpm.

Answer:

a. \(\sigma < 10\) bpm
b. \(H_0:\sigma = 10\) bpm, \(H_1:\sigma<10\) bpm