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​ food-borne illnesses,

76% were infected with a particular bacterium.

​a) Construct a 95% confidence interval.

Answer 1

solution:

sample size = n = 550

proportion of chickens infected with the becteria = = 76% = 0.76

confidence level = 95% = 0.95

so, = 1 - 0.95 = 0.05

critical value of z =           (from z table)

margin of error :

confidence interval:

lower limit = 0.76 - 0.0357 = 0.7243

upper limit = 0.76 + 0.0357 = 0.7957

so, confidence interval is   0.7243 < p < 0.7957