Question

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

Answer 1

Complete Question

In a study of the accuracy of fast food drive-through orders, one restaurant had 32 orders that were not accurate among 367 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?

Answer:

The decision rule  is

  Fail to reject the null hypothesis

The conclusion is  

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

Step-by-step explanation:

Generally from the question we are told that

   The sample size is  n =  367

    The number of orders that were not accurate is  $k = 32$

    The population proportion for rate of inaccurate orders is  p = 0.10

The null hypothesis is  $H_o : p = 0.10$

The alternative hypothesis is  $H_a : p \ne 0.10$

Generally the sample proportion is mathematically represented as  

         $\^ p = \frac{k}{n}$

=>      $\^ p = \frac{32}{367}$

=>      $\^ p = 0.0872$

Generally the test statistics is mathematically represented as

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

=>      $z= \frac{ 0.0872 - 0.10 }{ \sqrt{ \frac{ 0.10 (1 - 0.10 )}{367} } }$  

=>      $z= -0.8174$

From the z table  the area under the normal curve to the left corresponding to  -0.8174 is  

         $P(z < -0.8173 ) = 0.20688$

Generally the p-value is mathematically represented as

         $p- value = 2 * 0.20688$

=>      $p- value = 0.4138$

From the value obtained we see that  $p-value > \alpha$ hence

The decision rule  is

  Fail to reject the null hypothesis

The conclusion is  

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