Question

In a study of the accuracy of fast food​ drive-through orders, one restaurant had 37 orders that were not accurate among 305 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 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.

A.

Fail to reject H0. There is sufficient evidence to warrant rejection of the claim that the rate of inaccurate orders is equal to​ 10%.

B. 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%.

C. Reject H0. There is not sufficient evidence to warrant rejection of the claim that the rate of inaccurate orders is equal to​ 10%.

D. Reject H0. 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%, the restaurant should work to higher that 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 is plausible that the inaccuracy rate is ​10%. This rate would be too highThis rate would be too high​, the restaurant should work to lower the rate.

Answer 1

Test statistic is z statistic because we always use z statistic when dealing with proportions

Using TI 84 calculator

press stat then tests then 1-PropZtest

enter the data

po = 0.10

x =37

n = 305

prop po

press enter, we get

test statistic = 1.24

p value = 0.215

Conclusion

Since p value is greater than significance level, so we failed to reject the null hyppothesis

this means that there is sufficient evidence to support the claim that proportion is equal to 10%

option B is correct

B. 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%.

Interpretation

Yes, accuracy rate is acceptable, but it is necessary to lower the inaccurate rate of 10%

option D

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 highThis rate would be too high​, the restaurant should work to lower the rate.