Question

In a survey of 5000 registered voters who reside in California, 2739 were found to be republican. Construct a confidence estimate for the true percentage of republicans among registered voters in California. Use a confidence level of 99%.

Answer 1

Answer and Step-by-step explanation:

given:

Sample size is: n =5000

The sample proportion is: Ṗ = 2739 / 5000 = 54.78%

And the critical value of z for 99% confidence interval is

Z = 2.58

For a 99 % confidence interval we use formula:

Ṗ ± z√(Ṗ(1- Ṗ)/n)

By putting the given values in this formula:

0.54 ± 2.58√(0.54(1-0.54)/5000)

= 0.54 ± 0.018

This gives us upper confidence limit of

0.54 + 0.018 =0.558 = 0.54%

This gives us lower confidence limit of

o.54 – 0.018 = 0.522 = 0.53%