Question

In a study of the accuracy of fast food​ drive-through orders, one restaurant had 39 orders that were not accurate among 327 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.

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____

Answer 1

Solution:

Here, we have to use one sample z test for the population proportion.

The null and alternative hypotheses for this test are given as below:

Null hypothesis: H0: the rate of inaccurate orders is equal to​ 10%.

Alternative hypothesis: Ha: the rate of inaccurate orders is not equal to ​10%.

H0: p = 0.10 versus Ha: p ≠ 0.10

This is a two tailed test.

We assume

Level of significance = α = 0.05

Test statistic formula for this test is given as below:

Z = (p̂ - p)/sqrt(pq/n)

Where, p̂ = Sample proportion, p is population proportion, q = 1 - p, and n is sample size

x = number of items of interest = 39

n = sample size = 327

p̂ = x/n = 39/327 = 0.119266055

p = 0.10

q = 1 - p = 0.90

Z = (p̂ - p)/sqrt(pq/n)

Z = (0.119266055 – 0.10)/sqrt(0.10*0.90/327)

Z = 1.1613

Test statistic = 1.1613

The test statistic for this hypothesis test is 1.16.

P-value = 0.2455

(by using z-table)

The​ P-value for this hypothesis test is 0.2455.

P-value > α = 0.05

So, we do not reject the null hypothesis

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