Question

In a study of the accuracy of fast food​ drive-through orders, one restaurant had 32 orders that were not accurate among 352 orders observed. Use a 0.05 significance level to test the claim that the rate of inaccurate orders is equal to​ 10%. Does the accuracy rate appear to be​ acceptable?

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 Upper H 0 There is not sufficient evidence to warrant rejection of the claim that the rate of inaccurate orders is equal to​ 10%.

B.

Reject Upper H 0 There is not sufficient evidence to warrant rejection of the claim that the rate of inaccurate orders is equal to​ 10%.

C.

Fail to reject

Upper H 0. There is sufficient evidence to warrant rejection of the claim that the rate of inaccurate orders is equal to​ 10%.

D.

Reject Upper H 0. 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%, it is plausible that the inaccuracy rate is 10%. This rate would be too high​, the restaurant should work to lower the 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 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.

D.Since there is sufficient evidence to reject the claim that the rate of inaccurate orders is equal to​ 10%, the inaccuracy rate is acceptable.

Answer 1

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: P = 0.10
Alternative hypothesis: P 0.10

Note that these hypotheses constitute a two-tailed test.

Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method, shown in the next section, is a one-sample z-test.

Analyze sample data. Using sample data, we calculate the standard deviation (S.D) and compute the z-score test statistic (z).

S.D = sqrt[ P * ( 1 - P ) / n ]

S.D = 0.01599
z = (p - P) /S.D

z = - 0.569

where P is the hypothesized value of population proportion in the null hypothesis, p is the sample proportion, and n is the sample size.

Since we have a two-tailed test, the P-value is the probability that the z-score is less than - 0.569 or greater than 0.569.

Thus, the P-value = 0.5694.

Interpret results. Since the P-value (0.5694) is greater than the significance level (0.10), we failed to reject the null hypothesis.

A) 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%.

A) 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 high​, the restaurant should work to lower the rate.