Question

A county commissioner must vote on a resolution that would commit substantial resources to the construction of a sewer in an outlying residential area. Her fiscal decisions have been criticized in the past, so she decides to take a survey of residents in her district to find out if they favor spending money for a sewer system. She will vote to appropriate funds only if she can be reasonably sure that a majority of the people in her district favor the measure. What hypotheses should she test?

Short answer

The null hypothesis (H0) is that 50% or less of the residents support the spending money on a sewer system. The alternative hypothesis (H1) is that more than 50% of residents support the spending money on a sewer system.

Step-by-step solution

- Identify the Null Hypothesis

This is the default assumption unless proven otherwise. The null hypothesis (H0) in this case is: '50% or less than the residents in her district favor the spending money for a sewer system'.

- Identify the Alternative Hypothesis

This is what the commissioner will accept if the null hypothesis is rejected based on the results of the survey. The alternative hypothesis (H1) in this case is: 'More than 50% of the residents in her district favor the spending money for a sewer system.'

- Conduct the Survey and Test the Hypotheses

The commissioner needs to carry out the survey sampling a representative part of her district's population. Then, she will calculate the percentage of respondents supporting the measure and use appropriate hypothesis testing methods to determine if the null hypothesis can be rejected or not.