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%

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 \\e 0.10`

Generally the sample proportion is mathematically represented as

`\^ p = (k)/(n)`

=>
`\^ p = (32)/(367)`

=>
`\^ p = 0.0872`

Generally the test statistics is mathematically represented as

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

=>
`z= \frac{ 0.0872 - 0.10 }{ \sqrt{ ( 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%