Mathematics, 03.11.2020 16:40 illl6266

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

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Answer from: kim3265

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?

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%

Answer from: Quest

b. the average rate of change of f(x) is less than the average rate of change of g(x).

step-by-step explanation:

since the length of the interval is the same in each case, we only need to compare the change in y-value to see which is greater.

f(-2) = -3f(1) = 6 . . . estimated from f(x) = (x+2)^2-3, which matches points on the graph (-1,-2) and (0, 1)

so the change in y-value for function f is (6 )) = 9.

the table tells us

g(-2) = 1g(1) = 31

so the change in y-value for function g is (31 -1) = 30.

the change in y-value of f(x) on the interval is less than the change in y-value of g(x) on the same interval, so the average rate of change of f(x) is less than the average rate of change of g(x).

Answer from: Quest

step-by-step explanation:

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