Question 1: What is meant by ‘chi-squared = 23.98, P<0.001?’
The accuracy is to two standard errors, and for a proportion the standard error is the square root of p(1 – p)/n. The maximum value of the standard error is when p = 0.5. Two percentage points is 0.02, so
0.022 = 22 × 0.5 × 0.5/n
n = 22 × 0.5 × 0.5/0.022 = 4 × 0.25/0.0004 = 2500
A sample of size 2,500 would give a confidence interval of at most two percentage points on each side of the estimate for any sample proportion.
Back to Exercise: estimation of sample size.
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Last updated: 3 February, 2020.