Question

Gangelt is a small town in the west of Köln and effected severely by COVID19 pandemic.

German researchers had conducted tests on 500 random residents of the town and found that 70 of them infected by the virus.

Construct a 95% confidence interval for the proportion of infected people for this town.

Answer 1

Tests indicated that out of 500 random residents, 70 were infected by the virus.

So, the sample proportion is 70/500, ie. 0.14.

Now, we have to construct a 95% confidence interval for the proportion of infected people in the town.

Now, we know that the confidence interval for population proportion is given by

Where, p is the given sample proportion, z is the z value corresponding to the given confidence interval, and n is the given sample size.1

Here,

n=500

p=0.14

For 95% confidence interval, z=1.96

So, putting these values in the above definition, we get

ie.

ie.

ie.

ie.

ie.

ie.

So, the 95% confidence interval for the population proportion is (0.11,0.17)