Question

Census ~ In 2020, Pew Research conducted a poll to examine how likely a person was to participate in the 2020 US Census based on their age. In a random sample of US adults aged 18 - 49 years old, 67.45% said they were likely to participate in the Census. The estimated standard error of the sample proportion is 0.0148.

A normal distribution can be used to model the sampling distribution of sample proportion. The researchers wish to construct a 95% confidence interval for the actual proportion of US adults aged 18 – 49 years old who said they were likely to participate in the Census.

What is the lower bound for the 95% confidence interval? Give your answer to 4 decimal places.

Your Answer:

Answer 1

Solution :

Given that,

Point estimate = sample proportion = = 0.6745

= 0.0148

At 95% confidence level

= 1 - 95%

=1 - 0.95

= 0.05

Z = Z0.05 = 1.645

Margin of error = E = Z *   

= 1.645 * 0.0148

= 0.0243

A 95% lower confidence interval for population proportion p is ,

- E

= 0.6745 - 0.0243 = 0.6502

lower bound = 0.6502