Question

In a survey of 3450 registered voters who reside in California, 1789 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 95%. Show your work.

Find the sample size needed to estimate the percentage of republicans among registered voters in California. Use a 0.03 margin of error; use a confidence level of 90%

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Answer 1

n = Total number of voters = 3450

x = Number of voters found to be republican = 1789

                              (Round to 4 decimal)

Confidence level = c = 0.95

95% confidence interval is

Where zc is z critical for (1+c) /2 = (1+0.95) /2 = 0.975

zc = 1.96                             (From statistical table of z values)

0.5019 < p < 0.5353                      (Round to 4 decimal)

50.19% < p < 53.53%

95% confidence estimate for the true percentage of republicans among registered voters in California is (50.19%,53.53%)

Margin of error = e = 0.03

confidence level = c = 0.90

z critical for (1+c) /2 = (1+0.90)/2 = 0.95

zc = 1.645                         (From statistical table of z values, average of 1.64 and 1.65)

n = 0.249654 * 3006.694

n = 750.6334

n ~ 751

Sample size needed to estimate the percentage of republicans among registered voters in California is 751.