Q1-8BSC - Elementary Statistics

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.

Step-by-Step Solution

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 1: Given information

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

Step 2: 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.

Step 3: 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.

\({H_1}:\sigma  > 11\)