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 constituents to find out whether they favor spending money for a sewer system. She will vote to appropriate funds only if she can be fairly certain that a majority of the people in her district favor the measure. What hypotheses should she test?

Short answer

H0: A majority of constituents do not favor the spending for a sewer system. H1: A majority of constituents favor the spending for a sewer system. The commissioner must collect data through a survey and perform a statistical analysis to determine whether the null hypothesis can be rejected or not. Based on the result of the hypothesis test, she will make her decision.

Step-by-step solution

Formulate the null hypothesis (H0)

The null hypothesis is the initial presumption that a proposition or claim is true. It represents a statement of no effect or no difference. In this scenario, it would be: 'A majority of the constituents do not favor the spending for a sewer system.'

Formulate the alternative hypothesis (H1)

The alternative hypothesis is the claim or contention we are willing to accept once we have found the null hypothesis to be false. Here it is: 'A majority of the constituents favor the spending for a sewer system.'

Gathering and analyzing data

After the hypotheses have been set, the data should be collected through a survey. Then, statistical analysis would be deployed to determine whether the null hypothesis could be rejected or not. If the null hypothesis is rejected, it indicates that a majority of the constituents favor the proposal.

Decision making

Based on the results of the hypothesis test, the commissioner will make her decision. If the null hypothesis is rejected, she will vote to appropriate funds as a significant majority support the measure. If the null hypothesis is not rejected, she will refrain from voting to appropriate funds.