Question

In a study of the accuracy of fast food drive-through orders, Restaurant Ahad 265 accurate orders and 61 that were not accurate a. Construct a 95% confidence interval estimate of the percentage of orders that are not accurate b. Compare the results from part (a) to this 95% confidence interval for the percentage of orders that are not accurate at Restaurant B 0.167<p <0.244. What do you conclude? a. Construct a 95% confidence interval. Express the percentages in decimal form <p<(Round to three decimal places as needed.) b. Choose the correct answer below O A. 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. B. No conclusion can be made because not enough information is given about the confidence interval for Restaurant B. OC. Since the two confidence intervals overlap, neither restaurant appears to have a significantly different percentage of orders that are not accurate OD. 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 1

a)

b) ans-> A)

Let p denotes the population proportion. Let o denotes the sample proportion and n denotes the sample size. Here, 61 f 0.2302, n = 265, standard error 0.230 * (1 – 0.230) 265 = 0.025859 0.0259 265 At 95 percent confidence level, Margin of error is p = (1-0) ME * 2 1-0.95 2 0.230 * (1 – 0.230) 265 * 20.025 = 0.230 * (1 – 0.230) * 1.959964 = 0.050683 0.051 265 n a 95 percent confidence interval for the population proportion p is ©* (1 - ) = P + * 2 1-0.95 2 n = 0.2302 + 0.230 * (1 – 0.230) 265 * 20.025 = 0.2302 + 0.230 * (1 – 0.230) * 1.959964 265 = 0.2302 +0.050683 = = (0.179506,0.280871) ~ (0.180,0.281)