Confidence Interval Math Example 4

Follow the full solution, then compare it with the other examples linked below.

Example 4

hard
To achieve a margin of error of E=3E=3 with 95% confidence, given ฯƒ=20\sigma=20, find the required sample size nn.

Solution

  1. 1
    Required sample size formula: n=(zโˆ—ฯƒE)2n = \left(\frac{z^* \sigma}{E}\right)^2
  2. 2
    Substitute: n=(1.96ร—203)2=(39.23)2=(13.07)2=170.8n = \left(\frac{1.96 \times 20}{3}\right)^2 = \left(\frac{39.2}{3}\right)^2 = (13.07)^2 = 170.8
  3. 3
    Round up: n=171n = 171 (always round up to ensure margin of error is no larger than required)

Answer

Required n=171n = 171 to achieve margin of error โ‰ค3\leq 3 with 95% confidence.
Sample size planning is done before data collection. The formula n=(zโˆ—ฯƒ/E)2n = (z^*\sigma/E)^2 shows that smaller required margin (tighter precision) demands larger samples quadratically. Always round up to ensure the margin of error requirement is met.

About Confidence Interval

A range of values, computed from sample data, that is likely to contain the true population parameter with a specified level of confidence.

Learn more about Confidence Interval โ†’

More Confidence Interval Examples

Example 1 medium

A sample of [formula] has [formula] and [formula]. Construct a 95% confidence interval for the popul

Example 2 hard

Compare 90% and 99% confidence intervals for [formula], [formula], [formula]. Calculate both and exp

Example 3 easy

A 95% CI for a population mean is [formula]. Find the sample mean [formula] and the margin of error

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