In a study of the accuracy of fast food drive-through orders, one restaurant had 40 orders that were not accurate among 307 orders observed. Use a 0.05 significance level to test the claim that the rate of inaccurate orders is greater than 10%. State the test result in terms of the claim. Identify the null and alternative hypotheses for this test The test statistic for this hypothesis test is? The P-value for this hypothesis test is? Identify the conclusion for this hypothesis test. State the test result in terms of the claim.

We conclude that the rate of inaccurate orders is greater than 10%.

Step-by-step explanation:

We are given that in a study of the accuracy of fast food drive-through orders, one restaurant had 40 orders that were not accurate among 307 orders observed.

Let p = population proportion rate of inaccurate orders

So, Null Hypothesis, : p 10%     {means that the rate of inaccurate orders is less than or equal to 10%}

Alternate Hypothesis, : p > 10%      {means that the rate of inaccurate orders is greater than 10%}

The test statistics that will be used here is One-sample z-test for proportions;

                          T.S.  =    ~ N(0,1)

where,  = sample proportion of inaccurate orders = = 0.13

           n = sample of orders = 307

So, the test statistics =    

                                    =  1.75

The value of z-test statistics is 1.75.

Also, the P-value of the test statistics is given by;

            P-value = P(Z > 1.75) = 1 - P(Z 1.75)

                          = 1 - 0.95994 = 0.04006

Now, at 0.05 level of significance, the z table gives a critical value of 1.645  for the right-tailed test.

Since the value of our test statistics is more than the critical value of z as 1.75 > 1.645, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.

Therefore, we conclude that the rate of inaccurate orders is greater than 10%.