Question

In a study of the accuracy of fast food drive-through orders one restaurant had 32 orders that were not accurate among 372 orders observed use a .10 significance level to test the claim the rate of an accurate orders is equal to 10% does the accuracy rate appear to be acceptable

Answer 1

To test the accuracy rate of fast food orders, we use a hypothesis test with a significance level of 0.10. The null hypothesis is that the rate is equal to 10%, and the alternative hypothesis is that it is not. We can calculate the test statistic and compare it to the critical values to make a decision.

To test the claim that the rate of accurate orders is equal to 10%, we can use a hypothesis test. Let's assume the null hypothesis, H0, is that the rate of accurate orders is 10%, and the alternative hypothesis, Ha, is that the rate is not 10%. We will use a one-proportion z-test to test the claim.

Step 1: Null hypothesis: H0: p = 0.10

Step 2: Alternative hypothesis: Ha: p ≠ 0.10

Step 3: Test statistic: Z = (x - np) / sqrt(np(1-p))

Step 4: Where x = number of inaccurate orders, n = total number of orders, and p = hypothesized proportion of accurate orders

Step 5: Significance level = 0.10

Step 6: If the test statistic falls within the critical region (determined using the significance level), we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.