A political analyst found 43% of 300 randomly selected republican voters feel that the federal government has too much power. Find the 95% confidence interval of the population proportion of republican voters who feel this way.

We want to determine 95% confidence interval of the population proportion of republican voters who feel that the federal government has too much power.

43% of 300 randomly selected republican voters feel that the federal government has too much power. This means that

p = 43/100 = 0.43

q = 1 - p = 1 - 0.43 = 0.57

n = 300

mean, u = np = 300 × 0.43 = 129

Standard deviation, s = √npq = √129×0.57 = 8.575

For a confidence level of 95%, the corresponding z value is 1.96. This is determined from the normal distribution table.

We will apply the formula

Confidence interval

= mean +/- z ×standard deviation/√n

It becomes

129 +/- 1.96 × 8.575/√300

= 129 +/- 0.9704

The lower end of the confidence interval is 129 - 0.9704 =128.0296

The upper end of the confidence interval is 129 + 0.9704 =129.9704

Therefore, with 95% confidence interval, the mean of the population proportion of republican voters who feel that the federal government has too much power is between 128.0296 and 129.9704