Question

Let us assume that we randomly choose a sample of 144 people. 51% of people from our sample reported having voted for candidate A in the 2004 election. Using this sample, find 95% confidence interval for the population proportion of those who voted for this candidate. Round to three digits.

Lower end of confidence interval:  

Upper end of confidence interval:

Answer 1

Solution:

The 95% confidence interval for population proportion is given as follows:

Where, p̂ is sample proportion, q̂ = 1 - p̂, n is sample size and Z(0.05/2) is critical z-value to construct 95% confidence interval.

Sample proportion of people who voted for candidate A in the 2004 election is given by,  p̂ = 51% = 51/100 = 0.51

q̂ = 1 - 0.51 = 0.49 and n = 144

Using Z-table we get, Z(0.05/2) = 1.96

Hence, 95% confidence interval for population proportion is,

Lower end of confidence interval : 0.428

Upper end of confidence interval : 0.592

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