Question

Of 525 broiler chickens purchased from various kinds of food stores in different regions of a country and tested for types of bacteria that cause​ food-borne illnesses, 45​% were infected with a particular bacterium

​a) Construct a 95​% confidence interval.

​b) Explain what your confidence interval says about chicken sold in the country.

​c) 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?

Answer 1

a) From standard normal tables, we have here:
P(-1.96 < Z< 1.96) = 0.95

Therefore the confidence interval now is obtained here as:

This is the required 95% confidence interval here.

b) As the whole confidence interval lies below 0.5 here, therefore we have sufficient evidence here at 95% confidence level that less than majority were infected with a particular bacterium here. The interpretation of the confidence interval here is that we are 95% confident that the true population proportion of broiler chickens which are infected lies in the above obtained confidence interval.

c) As we have here:
np = 525*0.45 = 236.25 > 5
n(1-p) = 525*0.55 = 288.75 > 5

As both the normality assumptions are satisified here. Therefore the sample size is large enough here. Therefore the criticism is not valid here.