\( 1 \leftarrow \) In a study of the accuracy of fast food drive-through orders, one restaurant had 30 orders that were not accurate among 366 orders observed. Use a 0.01 significance level to test the claim that the rate of inaccurate orders is equal to \( 10 \% \). Does the accuracy rate appear to be acceptable? Identify the null and alternative hypotheses for this test. Choose the correct answer below. A. \( H_{0}: p=0.1 \) \( H_{1}: p<0.1 \) B. \( H_{0}: p=0.1 \) \( H_{1}: p>0.1 \) C. \( H_{0}: p \neq 0.1 \) \( H_{1}: p=0.1 \) (C. \( H_{0}: p=0.1 \) \( H_{1}: p \neq 0.1 \) Identify the test statistic for this hypothesis test. The test statistic for this hypothesis test is (Round to two decimal places as needed.)

To determine the correct hypotheses for this test, we want to assess whether the proportion of inaccurate orders is different from \(10\%\). The null hypothesis (\(H_{0}\)) typically reflects a status quo or a claim we want to test against, while the alternative hypothesis (\(H_{1}\)) reflects our suspicion. Therefore, the correct choice is: C. \( H_{0}: p=0.1 \) \( H_{1}: p \neq 0.1 \) Now, about the test statistic! You can calculate it using the formula for a proportion: \[ z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1 - p_0)}{n}}} \] Where: - \(\hat{p} = \frac{\text{Number of errors}}{\text{Total orders}} = \frac{30}{366} \approx 0.0819\) - \(p_0 = 0.1\) - \(n = 366\) Inserting these values: \[ z = \frac{0.0819 - 0.1}{\sqrt{\frac{0.1(1 - 0.1)}{366}}} \] This calculates to approximately: \[ z \approx \frac{-0.0181}{0.0164} \approx -1.10 \] So, the test statistic for this hypothesis test is \( -1.10 \) (rounded to two decimal places). Now, in a nutshell, your hypotheses set you up to challenge the status quo, while the test statistic gives you a numerical way to weigh your suspicions! Keep it up, and you're on your way to mastering statistics!