Question

CHALLENGE ACTIVITY 5.3.1: Confidence intervals for population proportions. Critical values for quick reference during this activity. Confidence level Critical value 0.90 = 1.645 0.95 z* = 1.960 0.99 2.576 Jump to level 1 In a poll of 1000 randomly selected voters in a local election, 34 voters were against fire department bond measures. What is the 99% confidence interval? (Ex: 0.123 Ex: 0.1230 ] (smaller value, larger value] 2 Check Next Feedback

Answer 1

Solution:

Confidence interval for Population Proportion is given as below:

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

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

We are given

Number of items of interest = x = 34

Sample size = n = 1000

Sample proportion = p̂ = x/n = 34/1000 = 0.034

Confidence level = 99%

Critical Z value = 2.576

(by using z-table)

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

Confidence Interval = 0.034 ± 2.576* sqrt(0.034*(1 – 0.034)/ 1000)

Confidence Interval = 0.034 ± 2.576*0.005731

Confidence Interval = 0.034 ± 0.014763

Lower limit = 0.034 - 0.014763 = 0.019237

Upper limit = 0.034 + 0.014763 = 0.048763

Confidence interval = (0.019, 0.049)