Question

Construct a confidence interval of the population proportion at the given level of confidence.

x=540, n=1100​, 95​% confidence

The lower bound of the confidence interval is _______.

​(Round to three decimal places as​ needed.)

The upper bound of the confidence interval is_______.

​(Round to three decimal places as​ needed.)

Answer 1

Answer)

Given n = 1100

P = 540/1100

First we need to check the conditions of normality that is if n*p and n*(1-p) both are greater than 5 or not

N*p = 540

N*(1-p) = 560

As both are greater than 5, conditions are met and we can use standard normal z table to construct the interval

From z table, critical value z for 95% confidence level is 1.96

Margin of error is = z*√p*(1-p)/√n

MOE = 0.02954322737

Lower bound is P-MOE = 0.46136586352 = 0.461

Upper bound is P +MOE = 0.52045231828 = 0.52