Question

In a study of the accuracy of fast food​ drive-through orders, one restaurant had 36 orders that were not accurate among 324 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.

Answer 1

Answer:

We do not have sufficient evidence to reject the claim that ,the rate of inaccurate orders is equal to​ 10%.

Step-by-step explanation:

We want to use a 0.01 significance level to test the claim that the rate of inaccurate orders is equal to​ 10%.

We set up our hypothesis to get:

$H_0:p=0.10$------->null hypothesis

$H_1:p\ne0.10$------>alternate hypothesis

This means that: $p_0=0.10$

Also, we have that, one restaurant had 36 orders that were not accurate among 324 orders observed.

This implies that: $\hat p=\frac{36}{324}=0.11$

The test statistics is given by:

$z=\frac{\hat p-p_0}{\sqrt{\frac{p_0(1-p_0)}{n} } }$

We substitute to obtain:

$z=\frac{0.11-0.1}{\sqrt{\frac{0.1(1-0.1)}{324} } }$

This simplifies to:

$z=0.6$

We need to calculate our p-value.

P(z>0.6)=0.2743

Since this is a two tailed test, we multiply the probability by:

The p-value is 2(0.2723)=0.5486

Since the significance level is less than the p-value, we fail to reject the null hypothesis.

We do not have sufficient evidence to reject the claim that ,the rate of inaccurate orders is equal to​ 10%.