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 180 dishes, of which 90 were sent back to the kitchen by the executive chef. In the same period, the competing Sapphire team cooked a total of 113 dishes and had 65 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 86%. Round each answer to 4 decimal places. Do not round from one part to the next when performing the calculations, though.

1. Find the confidence interval.
2. Which of the following does your interval contain?
3. What does this mean in terms of the population proportions?
   • We are 86% confident that, on average, the Ruby team has had more dishes return than the Sapphire team.
   • We are 86% confident that, on average, the Ruby team has had just as many dishes return as the Sapphire team.
   • We are 86% confident that, on average, the Ruby team has had less dishes return than the Sapphire team.

• only negative values
• both positive and negative values
• only positive values