# In January 2007 Consumer, Reports published a study of bacterial contamination of chicken sold in the United States.  They purchased 525 broiler chickens from various stores in 23 states and tested them for bacterial contamination.  Lab tests indicated 83% of the chickens were contaminated with Campylobacter.How would you justify a claim by the USDA that the number of chickens tested was not large enough since 9 billion chickens are sold each year in the U.S.?What is the impact on the confidence interval estimate if a larger sample is used?

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1. In January 2007 Consumer, Reports published a study of bacterial contamination of chicken sold in the United States.  They purchased 525 broiler chickens from various stores in 23 states and tested them for bacterial contamination.  Lab tests indicated 83% of the chickens were contaminated with Campylobacter.
2. How would you justify a claim by the USDA that the number of chickens tested was not large enough since 9 billion chickens are sold each year in the U.S.?
3. What is the impact on the confidence interval estimate if a larger sample is used?
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Step 1

1.

The number of contaminated chicken is,

Step 2

Thus, the number of contaminated chicken is 435.75.

2.

It is given that the sample size of 525 broiler chickens from various stores in 23 states indicated that 83% of the chickens were contaminated with Campylobacter.

The population size is 9 billion but the sample size is 525. The sample size must be at least 5% or 10% of the population size. The sample size of 525 is below these two percentages.

But, the np is greater than or equal to 10.

Hence, the claim made by the USDA that the number of chickens tested was not large enough since 9 billion chickens were sold each year in the U.S. is justified.

Step 3

3.

Confidence interval:

...

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