In a cooking competition called Heaven's Kitchen, two teams compete against each other to serve a restaurant full of customers. The competitors cook dishes and send them to an executive chef, where it is either approved and sent to the customer, or is deemed unacceptable and sent back to the kitchen. The competition has run for the past 19 years. During the 9th annual Heaven's Kitchen competition, the Ruby team cooked a total of 131 dishes, of which 70 were sent back to the kitchen by the executive chef. In the same period, the competing Sapphire team cooked a total of 170 dishes and had 85 return. Construct a confidence interval to estimate the difference in the proportion of dishes sent back to the Ruby team and the proportion of dishes sent back to the Round each answer to 4 decimal places. Do not round from one part to the next when performing the calculations, though. a. Find the confidence interval. < P - P2 < b. Which of the following does your interval contain? O only positive values O only negative values O both positive and negative values What does this mean in terms of the population proportions?

College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter9: Counting And Probability
Section: Chapter Questions
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In a cooking competition called Heaven's Kitchen, two teams compete against each other to serve a
restaurant full of customers. The oompetitors cook dishes and send them to an executive chef, where it is
either approved and sent to the customer, or is deemed unacceptable and sent back to the kitchen. The
competition has run for the past 19 years.
During the 9th annual Heaven's Kitchen competition, the Ruby team cooked a total of 131 dishes, of which
70 were sent back to the kitchen by the executive chef. In the same period, the competing Sapphire team
cooked a total of 170 dishes and had 85 return. Construct a confidence interval to estimate the difference
in the proportion of dishes sent back to the Ruby team and the proportion of dishes sent back to the
Sapphire team. Use a confidence level of 80%.
Round each ansvwer to 4 decimal places. Do not round from one part to the next when performing the
calculations, though.
a. Find the confidence interval.
< Pi - Pa <
b. Which of the following does your interval contain?
O only positive values
O only negative values
O both positive and negative values
c. What does this mean in terms of the population proportions?
O We are 80% confident that, on average, the Ruby team has had less dishes return than the
Sapphire team.
O We are 80% confident that, on average, the Ruby team has had just as many dishes return as
the Sapphire team.
O We are 80% confident that, on average, the Ruby team has had more dishes return than the
Sapphire team.
Transcribed Image Text:In a cooking competition called Heaven's Kitchen, two teams compete against each other to serve a restaurant full of customers. The oompetitors cook dishes and send them to an executive chef, where it is either approved and sent to the customer, or is deemed unacceptable and sent back to the kitchen. The competition has run for the past 19 years. During the 9th annual Heaven's Kitchen competition, the Ruby team cooked a total of 131 dishes, of which 70 were sent back to the kitchen by the executive chef. In the same period, the competing Sapphire team cooked a total of 170 dishes and had 85 return. Construct a confidence interval to estimate the difference in the proportion of dishes sent back to the Ruby team and the proportion of dishes sent back to the Sapphire team. Use a confidence level of 80%. Round each ansvwer to 4 decimal places. Do not round from one part to the next when performing the calculations, though. a. Find the confidence interval. < Pi - Pa < b. Which of the following does your interval contain? O only positive values O only negative values O both positive and negative values c. What does this mean in terms of the population proportions? O We are 80% confident that, on average, the Ruby team has had less dishes return than the Sapphire team. O We are 80% confident that, on average, the Ruby team has had just as many dishes return as the Sapphire team. O We are 80% confident that, on average, the Ruby team has had more dishes return than the Sapphire team.
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