A job-placing agency claims that 73% of their clients find full-time jobs within a month of using their services. In a random sample of 220 people, it was found that 76% were able to find full-time employment within a month of joining the agency. Perform a test to determine whether more than 73% of the clientsfind full-time employment. Use a significance level of 1%.

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 critical value. Round your answer to 2 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 more than 73% of the clients find full-time employment within a month of joining the agency.
   • There is not sufficient evidence to support the claim that more than 73% of the clients find full-time employment within a month of joining the agency.
   • The sample data support the claim that more than 73% of the clients find full-time employment within a month of joining the agency.
   • We accept that more than 73% of the population find full-time employment within a month of joining the agency.