Question

A random sample of 100 preschool children in Camperdown revealed that only 60 had been vaccinated.a.Provide a 95% confidence interval for the proportion vaccinated in that suburb.b.Write a statement explaining your confidence interval.

a.Provide a 95% confidence interval for the proportion vaccinated in that suburb.

b.Write a statement explaining your confidence interval.

Answer 1

Part a

Confidence interval for Population Proportion is given as below:

Confidence Interval = P ± Z* sqrt(P*(1 – P)/n)

Where, P is the sample proportion, Z is critical value, and n is sample size.

We are given

x = 60

n = 100

P = x/n = 60/100 = 0.6

Confidence level = 95%

Critical Z value = 1.96

(by using z-table)

Confidence Interval = P ± Z* sqrt(P*(1 – P)/n)

Confidence Interval = 0.6 ± 1.96* sqrt(0.6*(1 – 0.6)/100)

Confidence Interval = 0.6 ± 1.96* 0.0490

Confidence Interval = 0.6 ± 0.0960

Lower limit = 0.6 - 0.0960 = 0.5040

Upper limit = 0.6 + 0.0960 = 0.6960

Confidence interval = (0.5040, 0.6960)

Part b

WE are 95% confident that the population proportion of vaccination will lies between 0.5040 and 0.6960.