Question

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 95% 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**

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.The overlap
suggests that there is no significant difference in the proportions
of packages of *Tyson* and *Perdue* chicken with
bacterial contamination.

**Question 3**. Find the 95% 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 95% 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**

The one- and two-sample procedures for analyzing the data are
equivalent; the results differ in this problem only because of
natural sampling variation.Different methods were used in the two
samples to detect bacterial
contamination. *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.

Answer #1

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