a news poll which estimated that 82% of all voters believe global warming exists had a margin of error of /- 3%. suppose an environmental group planning a follow-up survey on this issue wants to determine a 95% confidence interval with a margin of error of no more than 2%. how large a sample do they need? (for estimate of p use 0.82)

Question

contestada

Respuesta :

contexto1024 contexto1024 · Answer 1 · 2022-11-11T01:52:09+01:00

The needed sample size is 1419. Sample Size is defined as the number of observations in the study.

In the question we have ,

estimate value of all voters who believe global warming ( p) = 82% = 0.82

margin of error (M.E) = 2% = 0.02

confidence of interval is calculated by estimate point value and add or subtract margin of error .

here,we have the value of confidence of interval is 95% = 0.95

Margin of error formula is

M.E = Z × √(p(1-p)/n)

where, p --> is estimated value

n---> sample size , which we required

Z ----> is z-value for observation

for the confidence of interval level 95% , the Z-value is 1.96 exist.

put all value in above formula we get,

0.02 = 1.96 × sqrt( ( 0.82)(1-0.82)/n)

=> 0.02 = 1.96× √(0.82×0.18/n)

= 0.02/1.96 = √0.1476/n => 0.000104= 0.1476/n

=> n = 1419

So, sample size is large and it is 1419.

To learn more about margin error , refer:

https://brainly.com/question/10218601

#SPJ4