## In a recent issue of Consumer Reports, Consumers Union reported on their investigation of bacterial contamination…

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**. 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**. 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

**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**

Natural sampling variation is the only reason that

*Tyson* appears to have a higher proportion of packages with

bacterial contamination.We are 90% confident 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. *Tyson’s* sample

proportion is higher than *Perdue’s* so clearly

*Tyson* has the greater true proportion of contaminated

chicken.

**Question 5**. The results in questions 2 and 4

seem contradictory. Which method is correct: doing two-sample

inference, or doing one-sample inference

twice? **One submission only; no
exceptions**

two-sample inferenceone-sample inference

twice

**Question 6**. Why don’t the results

agree? **2 submission only; no
exceptions**

*Tyson* chicken is sold in less sanitary supermarkets.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-of-proportions procedure takes this into

account. Different methods were used

in the two samples to detect bacterial contamination.The one- and

two-sample procedures for analyzing the data are equivalent; the

results differ in this problem only because of natural sampling

variation.