Question

state the null and alternative hypotheses you would use to test the following situation.

an annual report showed that florida topped the nation with 24% of its motorist uninsured. after implementing several new programs during the last two years, the state reevaluated its percentage of uninsured motorists. determine the null and alternative hypotheses for a test to determine whether the proportion of uninsured motorists has decreased over the last two years.

\\( h_0 : p = 0.24 \\)
\\( h_1 : p > 0.24 \\)

\\( h_0 : p = 0.24 \\)
\\( h_1 : p \
eq 0.24 \\)

\\( h_0 : p = 0.24 \\)
\\( h_1 : p < 0.24 \\)

\\( h_0 : p > 0.24 \\)
\\( h_1 : p < 0.24 \\)

Explanation:

Step1: Understand Null Hypothesis

The null hypothesis (\(H_0\)) is a statement of no change or equality. Here, the original proportion of uninsured motorists is 24% (or \(p = 0.24\)). So, \(H_0: p = 0.24\).

Step2: Understand Alternative Hypothesis

The alternative hypothesis (\(H_1\)) tests the claim. The claim is that the proportion has decreased, so we test if \(p < 0.24\). So, \(H_1: p < 0.24\).

Step3: Match with Options

Looking at the options, the third option has \(H_0: p = 0.24\) and \(H_1: p < 0.24\), which matches our analysis.

Answer:

\(H_0: p = 0.24\)
\(H_1: p < 0.24\) (the third option in the list)