SOLUTION: An advertising firm states that 27% of households will buy something on the Internet next year. How large a sample is needed to be 92% confident that this proportion is within 5% o

Algebra ->  Statistics  -> Central-limit-theorem -> SOLUTION: An advertising firm states that 27% of households will buy something on the Internet next year. How large a sample is needed to be 92% confident that this proportion is within 5% o      Log On


   

Question 1178691: An advertising firm states that 27% of households will buy something on the Internet next year. How large a sample is needed to be 92% confident that this proportion is within 5% of true proportion.
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
What we want is
abs%28p%5B1%5D+-+p%29+%3C=+z%5B0.96%5D%2Asqrt%28%28p%281-p%29%29%2Fn%29+=+0.05+, and
==> +1.751%2Asqrt%28%280.27%2A0.63%29%2Fn%29+=+0.05+
==> sqrt%28%280.27%2A0.63%29%2Fn%29+=+0.05%2F1.751+
==> %280.27%2A0.63%29%2Fn+=+%280.05%2F1.751%29%5E2+
==> n%2F%280.27%2A0.63%29+=+%281.751%2F0.05%29%5E2

==> n+=+0.27%2A0.63%2A%281.751%2F0.05%29%5E2+=+208.61, to 2 d.p.
This then implies to choose a sample with a size of highlight%28209%29.
(Normal probabilities were taken from https://stattrek.com/online-calculator/normal.aspx.)