Question

In a study of the accuracy of fast food​ drive-through orders, one restaurant had 37 orders that were not accurate among 304 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. H0​:p=0.1 and H1​: p<0.1

B. H0​: p≠0.1 and H1​: p=0.1

C.H0​: p=0.1 and H1​: p>0.1

D. H0​: p=0.1 and H1​:p≠0.1

The test statistic for this hypothesis test is ___

Identify the conclusion for this hypothesis test.

Does the accuracy rate appear to be​ acceptable?

Answer 1

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

Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n)
z = (0.1217 - 0.1)/sqrt(0.1*(1-0.1)/304)
z = 1.26

P-value Approach
P-value = 0.2077

As P-value >= 0.1, fail to reject null hypothesis.

Yes, the accuracy appears acceptable