Question

In a study of the accuracy of fast food​ drive-through orders, Restaurant A had 249 accurate orders and that were not accurate. a. Construct a ​90% confidence interval estimate of the percentage of orders that are not accurate. b. Compare the results from part​ (a) to this ​90% confidence interval for the percentage of orders that are not accurate at Restaurant​ B:0.164< p <0.239. What do you​ conclude? a. Construct a 90​% confidence interval. Express the percentages in decimal form. nothingp nothing ​(Round to three decimal places as​ needed.) b. Choose the correct answer below. A. No conclusion can be made because not enough information is given about the confidence interval for Restaurant B. B. Since the two confidence intervals​ overlap, neither restaurant appears to have a significantly different percentage of orders that are not accurate. C. The lower confidence limit of the interval for Restaurant B is higher than the lower confidence limit of the interval for Restaurant A and the upper confidence limit of the interval for Restaurant B is also higher than the upper confidence limit of the interval for Restaurant A.​ Therefore, Restaurant B has a significantly higher percentage of orders that are not accurate. D. Since the upper confidence limit of the interval for Restaurant B is higher than both the lower and upper confidence limits of the interval for Restaurant​ A, this indicates that Restaurant B has a significantly higher percentage of orders that are not accurate. Click to select your answer(s).

Answer 1

Complete Question

In a study of the accuracy of fast food? drive-through orders, Restaurant A had  249 accurate orders and 80 that were not accurate.  

a. Construct a 90?% confidence interval estimate of the percentage of orders that are not accurate.  

b.  Compare the results from part? (a) to this 90?% confidence interval for the percentage of orders that are not accurate at Restaurant? B: 0.164< p <0.239. What do you? conclude?

 Choose the correct answer below.  

A. Since the two confidence intervals  overlap, neither restaurant appears to have a significantly different percentage of orders that are not accurate.  

B. The lower confidence limit of the interval for Restaurant B is higher than the lower confidence limit of the interval for Restaurant A and the upper confidence limit of the interval for Restaurant B is also higher than the upper confidence limit of the interval for Restaurant A. Therefore, Restaurant B has a significantly higher percentage of orders that are not accurate.  

C. No conclusion can be made because not enough information is given about the confidence interval for Restaurant B.  

D. Since the upper confidence limit of the interval for Restaurant B is higher than both the lower and upper confidence limits of the interval for Restaurant? A, this indicates that Restaurant B has a significantly higher percentage of orders that are not accurate.

Answer:

a

The  90?% confidence interval  is  $0.2041 < p < 0.282$

b

Option A is the correct option

Step-by-step explanation:

From the question we are told that  

      The sample size is  n  =  249+80  = 329

        The number that are not accurate is  k  = 80

Generally the sample proportion of orders  that are not accurate is  mathematically evaluated as

                   $\r p = \frac{ 80 }{329}$

                    $\r p = 0.243$

Given that the confidence level is 90% then the level of significance is mathematically evaluated as

              $\alpha = 100 -90$

              $\alpha = 10\%$

               $\alpha = 0.10$

Next we obtain the critical value of  $\frac{ \alpha }{2}$ from the normal distribution table, the value is  

               $Z_{\frac{\alpha }{2} } = 1.645$

Generally the margin of error is mathematically represented as

              $E = Z_{\frac{\alpha }{2} } * \sqrt{ \frac{\r p (1- \r p )}{n} }$

=>            $E = 1.645* \sqrt{ \frac{0.243 (1- 0.243 )}{329} }$

=>              $E = 0.0389$

Generally the 90% confidence interval is  mathematically represented as

         $\r p -E < p < \r p +E$

=>       $0.2041 < p < 0.282$

Comparing the two 90% confidence of restaurant A and B we see that they overlap and  Since the two confidence intervals overlap, neither restaurant appears to have a significantly different percentage of orders that are not accurate.