Question

In a study of the accuracy of fast food drive-through orders, one restaurant had 38 orders that were not accurate among 329 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. O A. Ho: p=0.1 Hyp#0.1 OB. Ho: p=0.1 H:p>0.1 | 0 C. Họ p = 0.1 H:p<0.1 OD. Ho:p*0.1 He: p=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.) Identify the P-value for this hypothesis test. The P-value for this hypothesis test is (Round to three decimal places as needed.) Identify the conclusion for this hypothesis test. O A. Reject Ho. There is not sufficient evidence to warrant rejection of the claim that the rate of inaccurate orders is equal to 10%. OB. Fail to reject Ho. There is not sufficient evidence to warrant rejection of the claim that the rate of inaccurate orders is equal to 10%. O C. Reject Ho. There is sufficient evidence to warrant rejection of the claim that the rate of inaccurate orders is equal to 10%. O D. Fail to reject Ho. There is sufficient evidence to warrant rejection of the claim that the rate of inaccurate orders is equal to 10%.

Answer 1

Given that, n = 329 and x = 38

=> sample proportion $(\hat p)$ = 38/329 = 0.1155

The null and alternative hypotheses are,

H0 : p = 0.1

H1 : p ≠ 0.1

Test statistic is,

$Z = \frac { 0.1155-0.1}{\sqrt {\frac {0.1*(1-0.1)}{329}}} = 0.94$

The test statistic for this hypothesis test is 0.94

p-value = 2 * P(Z > 0.94) = 2 * 0.1736 = 0.3472

The P-value for this hypothesis test is 0.347

Since, p-value > 0.10, we fail to reject the null hypothesis.

=> Fail to reject H0. There is not sufficient evidence to warrant rejection of the claim that the rate of inaccurate orders is equal to 10%.

Since there is not sufficient evidence to reject the claim that the rate of inaccurate orders is equal to 10%, it is plausible that the inaccuracy rate is 10%. This rate would be too high, the restaurant should work to lower the rate.