Question

The Mamestra brassicae a moth is primarily known as a pest that is responsible for severe crop damage on a wide variety of plant species. Because there are limited means of chemically controlling the species, the use of wasp species that parasitize the eggs is used to control the reproduction and hence presence of these moths in agricultural crops. At a farm where a wasp species was introduced the eggs of the moths where collected and examined to determine if the wasps had successfully parasitized the eggs of the moths. Of 100 eggs collected 64 were determined to have been taken over by the wasps. Determine the 95% confidence interval for the true proportion moth eggs parasitized by the wasps.

Answer 1

The 95% confidence interval for the true proportion moth eggs parasitized by the wasps is;

CI = (0.5459, 0.7341)

We are given;

Sample size; n = 100

Number of successes in the sample; x = 64

Now, formula for estimated proportion of success is; p = x/n

p = 64/100

p = 0.64

Formula for confidence interval of proportions is;

CI = p ± z√(p(1 - p)/n)

Where z is the critical value at the confidence level.

From tables, at 95% CL, critical value z = 1.96

Thus;

CI = 0.64 ± 1.96√(0.64(1 - 0.64)/100)

CI = 0.64 ± 0.0941

Thus;

CI = (0.64 - 0.0941), (0.64 + 0.0941)

CI = (0.5459, 0.7341)

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