Question

In: Statistics and Probability

Of 525 broiler chickens purchased from various kinds of food stores in different regions of a...

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?

Solutions

Expert Solution

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.


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