Question

​Claim: The standard deviation of pulse rates of adult males is less than 10 bpm. For a random sample of 125 adult​ males, the pulse rates have a standard deviation of 9.5 bpm. Complete parts​ (a) and​ (b) below. a. Express the original claim in symbolic form. b. Find the value of the test statistic.

Answer 1

a.
`H0: g=10\\H1: g < 10`

b.
`X^2=111.91`

Explanation:

To express the original claim in symbolic form, we need to write the null and alternative hypothesis as:

`H0: g=10\\H1: g < 10`

Where
`g` is the standard deviation of the population and we want to know if the standard deviation of pulse rates of adult males is less than 10 bpm.

Then, the value of the test statistic
`X^2` with (n-1) degrees of freedom can be calculated as:

`X^2=((n-1)s^2)/(g^2)`

Where n is the size of the sample and s is the standard deviation of the sample. So, replacing values, we get:

`X^2=((125-1)9.5^2)/(10^2)=111.91`