In: Statistics and Probability
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.
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.