A food distribution company claims that a fast food restaurant chain receives, on average, 25 pounds of meat on a daily basis. The district manager of the restaurant chain decides to randomly sample 37 shipments from the company and finds a mean weight of 23.5 pounds with a standard deviation of 4.5 pounds. Test at a 1% level of significance to determine whether or not the food distribution company sends less than they claim.

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.
   
   $\displaystyle {H}_{{{0}}}$: 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 the food distribution company sends less than $\displaystyle {25}$ pounds of meat daily.
   • There is not sufficient evidence to support the claim that the food distribution company sends less than $\displaystyle {25}$ pounds of meat daily.
   • The sample data support the claim that the food distribution does not send $\displaystyle {25}$ pounds of meat daily.
   • We accept the food distribution company's claim.