Question

In: Statistics and Probability

Of 575 broiler chickens purchased from various kinds of food stores in different regions of a...

Of 575 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, 66% were infected with a particular bacterium. Construct a 95% confidence interval and explain what your confidence interval says about chicken sold in the country.

Solutions

Expert Solution

Solution :

Given that,

n = 575

Point estimate = sample proportion = = 0.66

1 - = 1 - 0.66 = 0.34

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96

Margin of error = E = Z / 2 * (( * (1 - )) / n)

= 1.96 * (((0.66 * 0.34) / 575)

= 0.039

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.66 - 0.039 < p < 0.66 + 0.039

0.621 < p < 0.699

(0.621 , 0.699)

A 95% confidence interval of chicken sold in the country is : (0.621 , 0.699)


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