In a recent issue of Consumer Reports, Consumers Union reportedon their investigation of bacterial contamination in packages ofname brand chicken sold in supermarkets. Packages of Tyson andPerdue chicken were purchased. Laboratory tests found campylobactercontamination in 35 of the 75 Tyson packages and 22 of the 75Perdue packages.

Question 1. Find 90% confidence intervals forthe proportion of Tyson packages with contamination and theproportion of Perdue packages with contamination (use 3 decimalplaces 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 inquestion 1 overlap. What does this suggest about the difference inthe proportion of Tyson and Perdue packages that have bacterialcontamination? One submission only; no exceptions

The overlap suggests that there is no significant difference inthe proportions of packages of Tyson and Perdue chicken withbacterial contamination.

Even though there is overlap, Tyson's sample proportion ishigher than Perdue's so clearly Tyson has the greater trueproportion of contaminated chicken.

Question 3. Find the 90% confidence intervalfor the difference in the proportions of Tyson and Perdue chickenpackages that have bacterial contamination (use 3 decimal places inyour answers).

_____ lower bound of confidence interval

_____ upper bound of confidence interval

Question 4. What does this interval suggestabout the difference in the proportions of Tyson and Perdue chickenpackages with bacterial contamination? One submission only; noexceptions

We are 90% confident that the interval in question 3 capturesthe true difference in proportions, so it appears that Tysonchicken has a greater proportion of packages with bacterialcontamination than Perdue chicken.

Natural sampling variation is the only reason that Tyson appearsto have a higher proportion of packages with bacterialcontamination.

Tyson's sample proportion is higher than Perdue's so clearlyTyson has the greater true proportion of contaminated chicken.

Question 5. The results in questions 2 and 4seem contradictory. Which method is correct: doing two-sampleinference, or doing one-sample inference twice? One submissiononly; no exceptions

two-sample inference

one-sample inference twice

Question 6. Why don't the results agree? 2submission only; no exceptions

The one- and two-sample procedures for analyzing the data areequivalent; the results differ in this problem only because ofnatural sampling variation.

If you attempt to use two confidence intervals to assess adifference between proportions, you are adding standard deviations.But it's the variances that add, not the standard deviations. Thetwo-sample difference-of-proportions procedure takes this intoaccount.

Different methods were used in the two samples to detectbacterial contamination.

Tyson chicken is sold in less sanitary supermarkets.