Question

A survey of 1000 randomly selected American adults found that 550 of them feel happy about their lives.

a. In this survey, the sample proportion of American adults who feel happy about their lives is:

a. A 95% confidence interval for the true percent of all American adults who feel happy about their lives is given by:

Answer 1

This is an example of binomial distribution where

X: American adults who are happy

n: Sample size

(1) Sample proportion

= 550 / 1000

(2) We use a normal approximation for true binomial proportion size the sample size is large (> 30)

95% confidence interval is given by

where the Critical value =

Alpha = 1 - 95% = 0.05

= 1.96 ..................Using normal percentage tables

Substituting all the values

This means that we are 95% confident that the true proportion of American adults happy with their lives lie within (0.5192, 0.5808).