Question

In a study of the accuracy of fast food​ drive-through orders, one restaurant had 32 orders that were not accurate among 398 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 H1​: p=0.1

B. H0​: p=0.1 H1​: p≠0.1

C. H0​: p=0.1 H1​: p<0.1

D. H0​: p=0.1 H1​: p>0.1

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

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

D. 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%.

Does the accuracy rate appear to be​ acceptable?

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

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 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

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H₀ : p = 0.10

H_a : p 0.10

n = 398

x = 32

= x / n = 32 / 398 = 0.0804

P₀ = 0.10

1 - P₀ = 1 - 0.10 = 0.90

z = - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.0804 - 0.10 / [(0.10 * 0.90) / 398]

= -1.303

The test statistic for this hypothesis test is = -1.30

This is the right tailed test .

P(z < -1.303) = 0.0968

P-value = 2 * P(z < -1.303) = 2 * 0.0968 = 0.1936

The​ P-value for this hypothesis test is = 0.194

= 0.10

P-value >

D. 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%.

D. 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