Answer:
Step-by-step explanation:
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
= 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
