Question

In a study of the accuracy of fast food​ drive-through orders, one restaurant had 30 orders that were not accurate among 379 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. Upper H 0​: pequals0.1 Upper H 1​: pnot equals0.1

B. Upper H 0​: pnot equals0.1 Upper H 1​: pequals0.1

C. Upper H 0​: pequals0.1 Upper H 1​: pgreater than0.1

D. Upper H 0​: pequals0.1 Upper H 1​: pless than0.

1 Identify the test statistic for this hypothesis test. The test statistic for this hypothesis test is -1.35 negative 1.35. ​(Round to two decimal places as​ needed.)

Identify the​ P-value for this hypothesis test. The​ P-value for this hypothesis test is 0.177 0.177. ​(Round to three decimal places as​ needed.)

Identify the conclusion for this hypothesis test. A. 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. 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%. C. 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. 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%.

Does the accuracy rate appear to be​ acceptable? A. Since there is sufficient evidence to reject the claim that the rate of inaccurate orders is equal to​ 10%, the inaccuracy rate is acceptable. 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 not sufficient evidence to reject the claim that the rate of inaccurate orders is equal to​ 10%, the restaurant should work to higher that rate. D. 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.

Answer 1

a)

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p = 0.1
Alternative Hypothesis, Ha: p ≠ 0.1

b)

Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n)
z = (0.0792 - 0.1)/sqrt(0.1*(1-0.1)/379)
z = -1.35

P-value Approach
P-value = 0.177

As P-value >= 0.05, fail to reject null hypothesis.

D. 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%.

D. 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.