Question

In: Statistics and Probability

In a study of the accuracy of fast food​ drive-through orders, one restaurant had 36 orders...

In a study of the accuracy of fast food​ drive-through orders, one restaurant had 36 orders that were not accurate among 313 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.

Identify the test statistic for this hypothesis test.

Identify the conclusion for this hypothesis test.

A.

Fail to reject

Upper H 0H0.

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

B.

Reject

Upper H 0H0.

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

C.

Fail to reject

Upper H 0H0.

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

D.

Reject

Upper H 0H0.

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 not sufficient evidence to disprove the theory that the rate of inaccurate orders is equal to​ 10%, the accuracy rate is not acceptable. The restaurant should work to lower that rate.

B.Since there is not sufficient evidence to disprove the theory that the rate of inaccurate orders is equal to​ 10%, it is possible that the accuracy rate is acceptable.

C.Since there is sufficient evidence to disprove the theory that the rate of inaccurate orders is equal to​ 10%, the accuracy rate is not acceptable. The restaurant should work to lower that rate.

D.Since there is sufficient evidence to disprove the theory that the rate of inaccurate orders is equal to​ 10%, the accuracy rate is acceptable.

Solutions

Expert Solution

The null and alternative hypotheses for this test are

H0: p = 0.10

Ha: p 0.10

np(1-p) = 313 * 0.1 * (1 - 0.1) = 28.17

Since np(1-p) > 10, the sample size is large enough to approximate the sampling distribution of proportion as normal distribution and conduct a one sample z test.

Standard error of sample proportion, SE = = 0.016957

Sample proportion, = 36/313 =  0.115016

Test statistic, z = ( - p) / SE = (0.115016 - 0.10)/0.016957 =  0.8855

For two-tail test, p-value = 2 * P(z > 0.8855) = 0.3759

Since, p-value is greater than 0.01 significance level, we fail to reject null hypothesis H0 and conclude that there is no significant evidence from the data that to reject the claim that the rate of inaccurate orders is equal to​ 10%

C.

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%.

B.Since there is not sufficient evidence to disprove the theory that the rate of inaccurate orders is equal to​ 10%, it is possible that the accuracy rate is acceptable.


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