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In a survey of 5000 registered voters who reside in California, 2739 were found to be republican. Construct a confidence estimate for the tr
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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%.
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2021-08-19T04:35:42+00:00
2021-08-19T04:35:42+00:00 1 Answers
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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%