Question

Male Pulse Rates and Age Using the pulse rates of males from Data Set 1 “Body Data” in Appendix B after they are partitioned into the three age brackets of 18–25, 26–40, and 41–80, we get the following SPSS display. Using a 0.05 significance level, test the claim that males from the three age brackets have the same mean pulse rate. What do you conclude?Male Pulse Rates and Age Using the pulse rates of males from Data Set 1 “Body Data” in Appendix B after they are partitioned into the three age brackets of 18–25, 26–40, and 41–80, we get the following SPSS display. Using a 0.05 significance level, test the claim that males from the three age brackets have the same mean pulse rate. What do you conclude?

Short answer

It can be concluded with a p-value of 0.275 that mean pulse rates of all age brackets of males are equal at a 0.05 significance level.

Step-by-step solution

Given information

The mean pulse rates of three age brackets of males is compared; 18-25,26-40 and 41-80 using the outputs from SPSS.

The claim is that the mean pulse rates of the males in three age brackets are the same.

The significance level is 0.05.

Explain the test ANOVA

The base hypotheses compared using ANOVA are:

\(\begin{aligned}{l}{H_o}:{\mu _1} = {\mu _2} = {\mu _3} = ... = {\mu _n}\\{H_a}:\;{\rm{atleast}}\;{\rm{one}}\;{\mu _i}\;{\rm{is}}\;{\rm{different}}\end{aligned}\)

Where\({\mu _i}\)are mean values for different groups.

The criteria to derive while conducting ANOVA:

• If the p-value is larger than 0.05, the null hypothesis is failed to be rejected; hence, the result is insignificant.
• If the p-value is smaller than 0.05, the null hypothesis is rejected, and hence the result is significant.

Frame the statistical hypothesis

Define three groups mean pulse rates for males\({\mu _1},{\mu _2},{\mu _3}\)for the three age brackets 18-25, 26-40, and 41-80, respectively.

The null hypothesis and the alternative hypothesis is,

\(\begin{aligned}{l}{H_o}:{\mu _1} = {\mu _2} = {\mu _3}\\{H_a}:\;{\rm{atleast}}\;{\rm{one}}\;{\rm{of}}\;{\rm{the}}\;{\mu _i}\;{\rm{is}}\;{\rm{different}}\end{aligned}\)

Determine the conclusion

From the output, the p-value is obtained from the last column named significance which is 0.275

As the p-value exceeds 0.05, the null hypothesis is failed to be rejected at the 0.05 significance level.

Therefore, there is enough evidence to support the claim that the males from the three age brackets have the same mean pulse rates.

Thus, it can be concluded that at 0.05 level of significance, the mean level of pulse rate for all age brackets to which males belong is equal. Thus, the male's pulse rates are not affected by the age brackets.