Question

A survey aims to find the proportion of the voting population in favour of a government referendum proposal to abolish the Nexus Rule (between Senate numbers and those in the House of Representatives). They obtain a random sample of 2000 voters to find their opinion and the sample indicates 953 are in favour of the change.

a. (i) State the estimated proportion in favor.

(ii) Find a 95% confidence interval for the proportion in favor. Is the referendum likely to fail?

b. How large a sample would be needed to give an estimate of the population proportion in favor to within ±0.05 with 95% confidence?

Answer 1

Solution:

We are given,

n = 2000

x = 953

a)

i) We have to find estimated proportion in favor ( Sample proportion ):

= x / n = 953 / 2000

= 0.48

ii) We have to Find 95% CI for proportion in favor:

Level of Confidence = 95%
α = 100% - (Level of Confidence) = 5%
α/2 = 2.5% = 0.025

z_α/2 = 1.96

Lower Bound = p̂ - z_α/2•√p̂(1 - p̂)/n = 0.4581

Upper bound = p̂ + z_α/2•√p̂(1 - p̂)/n = 0.5019

Hence Confidence Interval = ( 0.4581 , 0.5019 )

b) We have to find Sample size using formula:

Given, Margin of error = E = 0.05

Keeping all values in formula:

n = 384

Hence we needed 34 sample size.

Done