In a recent issue of Consumer Reports, Consumers Union reported on their investigation of bacterial contamination in packages of name brand chicken sold in supermarkets.

Packages of Tyson and Perdue chicken were purchased. Laboratory tests found campylobacter contamination in 35 of the 75 Tyson packages and 22 of the 75 Perdue packages.

Question 1. Find 90% confidence intervals for the proportion of Tyson packages with contamination and the proportion of Perdue packages with contamination (use 3 decimal places in your answers).

lower bound of Tyson interval

upper bound of Tyson interval

lower bound of Perdue interval

upper bound of Perdue interval

Question 2. The confidence intervals in question 1 overlap. What does this suggest about the difference in the proportion of Tyson and Perdue packages that have bacterial contamination? One submission only; no exceptions

The overlap suggests that there is no significant difference in the proportions of packages of Tyson and Perdue chicken with bacterial contamination. Even though there is overlap, Tyson's sample proportion is higher than Perdue's so clearly Tyson has the greater true proportion of contaminated chicken.

Question 3. Find the 90% confidence interval for the difference in the proportions of Tyson and Perdue chicken packages that have bacterial contamination (use 3 decimal places in your answers).

lower bound of confidence interval

upper bound of confidence interval