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of 550 broiler chickens purchased from various kinds of food stores in different

ID: 3366708 • Letter: O

Question

of 550 broiler chickens purchased from various kinds of food stores in different regions of a country and tested for types of bacteria that cause foodborne illness. 47% were infected with a particular bacterium.


1. Construct a 95% confidence interval

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

3. A government spokesperson claimed that the sample size was too small, relative to the billions of chickens slaughtered each year, to generalize. Is this criticism valid?


Explanation / Answer

Result:

of 550 broiler chickens purchased from various kinds of food stores in different regions of a country and tested for types of bacteria that cause foodborne illness. 47% were infected with a particular bacterium.

1. Construct a 95% confidence interval

CI for proportion

p =0.47, n=550

Z value for 95% = 1.96

CI = p pm z* sqrt {(p*(1-p)/n)}

CI = 0.47 pm 1.96* sqrt{(0.47*(1-0.47)/550)}

=( 0.4283, 0.5117)

95% confidence interval =(0.4283, 0.5117) or

(42.83% to 51.17%)

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

We are 95% confident that chickens purchased in all regions infected with a particular bacterium falls in the interval (42.83% to 51.17%).

3. A government spokesperson claimed that the sample size was too small, relative to the billions of chickens slaughtered each year, to generalize. Is this criticism valid?

No, as long as the necessary assumptions and conditions were met, the results can be generalized.