Final answer:
A hypothesis test at the 5 percent significance level would involve comparing the survey percentages of heart failure by age group to the national percentages using a chi-square test for goodness of fit. If the calculated chi-square statistic exceeds the critical value, the null hypothesis is rejected, indicating the sample is not representative.
Step-by-step explanation:
The student is asking how to perform a hypothesis test at the 5 percent significance level to determine whether the survey participants are a representative sample of the population with heart failure nationwide. To accomplish this, one would need to first establish the null hypothesis which in this case would assert that there is no significant difference between the survey percentages and the national percentages. The alternative hypothesis would claim that there is a significant difference.
Using the given percentages from Table 11.42 and the corresponding age groups, one would calculate the expected frequencies based on the national percentages and then compare them to the actual frequencies obtained in the survey.
This can be done using a chi-square test for goodness of fit. The calculated chi-square statistic would then be compared to the critical value from the chi-square distribution with the appropriate degrees of freedom. If the calculated value is greater than the critical value, the null hypothesis is rejected, indicating that the sample is not representative of the national population in terms of heart failure prevalence by age group.