In a small town in Colorado, it was found that 58% of the population support Candidate Randy. In a random sample of 100 residents of this small town, it was found that 50 of them support Randy. Perform a test to determine if less than 58% of the population support Randy. Use a significance level of 0.02%.

1. Check all of the requirements that are satisfied.
   
   • random
   • the $\displaystyle \overline{{{x}}}$ distribution is normal since $\displaystyle {n}\ge{30}$
   • the $\displaystyle \overline{{{x}}}$ distribution is normal since the $\displaystyle {x}$ distribution is normal
   • the $\displaystyle \hat{{{p}}}$ distribution is normal since $\displaystyle {n}{p}\ge{10}$ and $\displaystyle {n}{q}\ge{10}$
2. Identify the null and alternative hypotheses. Enter the parameter as a decimal.
   
   $\displaystyle {H}_{{{0}}}$: Select an answer p p̂ x̄ s μ σ σ² s² ? < > ≠ =
   
   $\displaystyle {H}_{{{1}}}$: Select an answer p p̂ x̄ s μ σ σ² s² ? < > ≠ =
   
   
3. What type of hypothesis test should you conduct (left, right, or two-tailed)?
   
   • left-tailed
   • right-tailed
   • two-tailed
4. Identify the appropriate significance level. Make sure to enter your answer as a decimal.
   
   
   
5. Which calculator function should you use? Select an answer 1-PropZInt 1-PropZTest ZInterval Z-Test TInterval T-Test invNorm
   
   
6. Find the test statistic. Write the result below, and be sure to round your final answer to two decimal places.
   
   
   
7. Find the p-value. Enter your answer as a decimal (not a percentage) and round to 4 decimal places.
   
   
   
8. Should you reject or not reject the null hypothesis?
   
   • reject the null hypothesis since $\displaystyle {p}$-value $\displaystyle \le\alpha$
   • do not reject the null hypothesis since $\displaystyle {p}$-value $\displaystyle >\alpha$
   • reject the null hypothesis since the test statistic is inside the critical region
   • do not reject the null hypothesis since the test statistic is outside the critical region
   
   
   
9. Select the statement below that best represents the interpretation.
   
   • There is sufficient evidence to support the claim that less than 58% of the population support Randy.
   • There is not sufficient evidence to support the claim that less than 58% of the population support Randy.
   • The sample data support the claim that less than 58% of the population support Randy.
   • We accept that less than 58% of the population support Randy.