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 7S Tyson packages and 22 of the 75 Perdue packages. Question 1. Determine 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. (True/False) The confidence intervals in question 1 overlap. If someone concluded that this overlap of the confidence intervals Implies that there is no significant difference between the proportions of Tyson and Perdue packages that are contaminated, they would be correct. One submission only; no exceptions 0 True 0 False Ques n 3. Find the 90% condence 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 Question 4. What does this interval suggest about the difference in the proportions of Tyson and Perdue chicken packages with bacterial contamination? One submission only; no exceptions 0 We are 90% condent that the interval in question 3 captures the true difference in proportions, so it appears that Tyson chicken has a greater proportion of packages with bacterial contamination than Perdue chicken. 0 Tyson's sample proportion is higher than Perdue's so clearly Tyson has the greater true proportion of contaminated chicken. 0 Natural sampling variation is the only reason that Tyson appears to have a higher proportion of packages with bacterial contamination. Question 5. The overlap of the two confidence intervals in question 1 and the entirely positive single confidence interval in question 4 suggest two conclusions that are contradictory. which method is correct: - constructing two single-sample condence intervals. one for each proportion as in question 1 and noting if they overlap or - constructing one oondence interval for the diiference in proportions as in question 4. and noting if the interval is entirely positive. entirely negative. or oonlains 0. One submission only. 0 Constructing one condence interval for the difference in proportions as in question 4. 0 Constructing two single-sample confidence intervals, one for each proportion as in question 1. Question 5. Why don't the results agree? 2 submi snon only; no exceptions 0 Tyson chicken is sold in less sanitary supermarkets. Q If you attempt to use two confidence intervals to assess a difference between proportions, you are adding standard deviations. But it's the variances that add, not the standard deviations. The two-sample difference-ofproportions procedure takes this into account. 0 Different methods were used in the two samples to detect bacterial contamination. O The one- and two-sample procedures for analyzing the data are equivalent; the results differ in this problem only because of natural sampling variation