Question

In a study of the accuracy of fast food​ drive-through orders, one restaurant had 40 orders that were not accurate among 306 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. Upper H 0​: pnot equals0.1 Upper H 1​: pequals0.1 B. Upper H 0​: pequals0.1 Upper H 1​: pless than0.1 C. Upper H 0​: pequals0.1 Upper H 1​: pgreater than0.1 D. Upper H 0​: pequals0.1 Upper H 1​: pnot equals0.1 Identify the test statistic for this hypothesis test. The test statistic for this hypothesis test is nothing. ​(Round to two decimal places as​ needed.) Identify the​ P-value for this hypothesis test. The​ P-value for this hypothesis test is nothing. ​(Round to three decimal places as​ needed.) Identify the conclusion for this hypothesis test. A. Fail to reject Upper H 0. There is not sufficient evidence to warrant rejection of the claim that the rate of inaccurate orders is equal to​ 10%. B. Reject Upper H 0. There is not sufficient evidence to warrant rejection of the claim that the rate of inaccurate orders is equal to​ 10%. C. Fail to reject Upper H 0. There is sufficient evidence to warrant rejection of the claim that the rate of inaccurate orders is equal to​ 10%. D. Reject Upper H 0. There is sufficient evidence to warrant rejection of the claim that the rate of inaccurate orders is equal to​ 10%. Does the accuracy rate appear to be​ acceptable? A. 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, so the restaurant should work to lower the rate. B. Since there is sufficient evidence to reject the claim that the rate of inaccurate orders is equal to​ 10%, the inaccuracy rate is​ unacceptable, so the restaurant should work to lower that rate. C. Since there is sufficient evidence to reject the claim that the rate of inaccurate orders is equal to​ 10%, the inaccuracy rate is acceptable. D. Since there is not sufficient evidence to reject the claim that the rate of inaccurate orders is equal to​ 10%, it appears that the inaccuracy rate is acceptable for the restaurant operations.

Answer 1

The statistical software output for this problem is:

Hence,

Hypotheses:

H₀ : p = 0.1
H_A : p ≠ 0.1

Test statistic = 1.79

P - value = 0.073

Conclusion: 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%. Option A is correct.

Does the accuracy rate appear to be​ acceptable?

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, so the restaurant should work to lower the rate. Option A is correct.