Question

In 2007, Consumer Report published a report of bacterial contamination of chicken sold in the US. They purchased 523 broiler chickens from various kinds of food stores, and tested them for bacteria that causes food-borne illnesses. Results indicated that 83% of chickens were infected with Campylobacter.

1. Construct a 95% confidence interval.

2. Explain what your confidence interval says about chicken sold in the US.

3. A spokesperson for the US Department of Agriculture dismissed the report, saying, “That’s 500 samples out of 9 billion chickens slaughtered a year…With the small numbers they tested, I don’t know that one would want to change one’s buying habits.” Is this criticism valid? Explain.

b. Find one aspect of this week’s material that is relevant to college, career, or everyday life. Provide some detail on how it could be important.

Answer 1

1. Construct a 95% confidence interval.

Solution:

Here, we have to find the confidence interval for the population proportion.

The formula for confidence interval for population proportion is given as below:

Confidence interval for Population Proportion

Confidence Interval = P ± Z* sqrt(P*(1 – P)/n)

Where, P is the sample proportion, Z is critical value, and n is sample size.

We are given

n = 523

P = 83% = 0.83

Confidence level = 95%

Critical Z value = 1.96

(by using z-table)

Confidence Interval = P ± Z* sqrt(P*(1 – P)/n)

Confidence Interval = 0.83 ± 1.96* sqrt(0.83*(1 – 0.83)/n)

Confidence Interval = 0.83 ± 1.96* 0.0164

Confidence Interval = 0.83 ± 0.0322

Lower limit = 0.83 - 0.0322 = 0.7978

Upper limit = 0.83 + 0.0322 = 0.8622

Confidence interval = (0.7978, 0.8622)

2. Explain what your confidence interval says about chicken sold in the US.

From above confidence interval, we can say that we are 95% confident that the population proportion of the chicken infected with Campylobacter will lies between 79.78% and 86.22%.

3. A spokesperson for the US Department of Agriculture dismissed the report, saying, “That’s 500 samples out of 9 billion chickens slaughtered a year…With the small numbers they tested, I don’t know that one would want to change one’s buying habits.” Is this criticism valid? Explain.

Answer: Yes, this criticism is valid, because the sample size is very small as compared to the population. We know that the results would be affected if the sample size is very small as compared to population size. There is a chance of biased estimates for the population proportion. So, it is required to increase the sample size for getting more unbiased results.

b. Find one aspect of this week’s material that is relevant to college, career, or everyday life. Provide some detail on how it could be important.

There are so many real life examples for which we use estimates for population proportion. Sometimes we say that the proportion of students getting pass the specific course is about 60 to 70 percent. Also, we say that the proportion of winning the football match by specific team is about 70 to 80 percent. There would be several everyday life examples which related with population proportion.