Problem
In a study of the accuracy of fast food drive-through orders, one restaurant had 31 orders that were not accurate among 368 orders observed. Use a 0.10 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. $\mathrm{H}_{0}: \mathrm{p}=0.1$ \[ \mathrm{H}_{1}: \mathrm{p}>0.1 \] B. \[ \begin{array}{l} H_{0}: p=0.1 \\ H_{1}: p \neq 0.1 \end{array} \] c. \[ \begin{array}{l} H_{0}: p \neq 0.1 \\ H_{1}: p=0.1 \end{array} \] D. \[ \begin{array}{l} H_{0}: p=0.1 \\ H_{1}: p<0.1 \end{array} \]
Solution
Step 1 ：Identify the null and alternative hypotheses for this test.
Step 2 ：The null hypothesis is always the statement that the parameter equals the claimed value. In this case, the claim is that the rate of inaccurate orders is equal to 10%, so the null hypothesis is that p = 0.1.
Step 3 ：The alternative hypothesis is the opposite of the null hypothesis. Since we are testing the claim that the rate of inaccurate orders is equal to 10%, the alternative hypothesis is that the rate is not equal to 10%.
Step 4 ：Therefore, the correct answer is B: \n\n\[\begin{array}{l}H_{0}: p=0.1 \H_{1}: p \neq 0.1\end{array}\]
