Question

In a study of the accuracy of fast food drive-through orders, one restaurant had 31 orders that were not accurate among 370 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. Choose the correct answer below.

A. Upper H0 : pequals=0.10.1 Upper H1 : pnot equals≠0.10.1

B. Upper H 0H0 : pequals=0.10.1 Upper H 1H1 : pgreater than>0.10.1

C. Upper H 0H0 : pequals=0.10.1 Upper H 1H1 : pless than<0.10.1

D. Upper H 0H0 : pnot equals≠0.10.1 Upper H 1H1 : pequals=0.10.1

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 rejectFail to reject Upper H0. There is notis not sufficient evidence to warrant rejection of the claim that the rate of inaccurate orders is equal to 10%. B. RejectReject Upper H 0H0. There is notis not sufficient evidence to warrant rejection of the claim that the rate of inaccurate orders is equal to 10%. C. RejectReject Upper H0. There is sufficient evidence to warrant rejection of the claim that the rate of inaccurate orders is equal to 10%. D. Fail to rejectFail 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%.

Does the accuracy rate appear to be acceptable?

A. Since there is notis 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, so the restaurant should work to lower the rate.

B. Since there is notis not sufficient evidence to reject the claim that the rate of inaccurate orders is equal to 10%, it appears that the inaccuracy rate is acceptable for the restaurant operations.

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 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.

Answer 1

Option - A) H₀: P = 0.10

H₁: P 0.10

= 31/370 = 0.084

The test statistic z = ( - P)/sqrt(P(1 - P)/n)

= (0.084 - 0.1)/sqrt(0.1 * 0.9/370)

= -1.03

P-value = 2 * P(Z < -1.03)

= 2 * 0.1515 = 0.303

Since the p-value is greater than the significance level (0.303 > 0.01), so we should not reject the null hypothesis.

Option - D) There is sufficient evidence to warrant rejection of the claim that the rate of inaccurate orders is equal to 10%.

Option - B) Since there is not sufficient evidence to reject the claim that the rate of inaccurate orders is equal to 10%, it appears that the inaccuracy rate is acceptable for the restaurant operations.