Question

A leading dental journal claims that 63% of young adults do not brush their teeth regularly. A dental hygienist wants to conduct a survey to verify this with her young adult patients, and wants to do so with a margin of error (ME) of ± 9%. What minimum sample size, rounded to the nearest whole person, does the hygienist need to use?

Answer 1

Margin of error = Z*Sqrt [p(1-p)/n]

Where
Z = Z-value at a given confidence interval (assume 1.96 for 95%)
p = point estimate = 63% = 0.63
n = sample size

Substituting;
0.09 = 1.96* Sqrt [0.63(1-0.63)/n]
(0.09/1.96)^1 = 0.63(1-0.63)/n = 0.2331/n
n = 0.2331/[(0.09/1.96)^2] = 110.55 ≈ 111

Therefore, minimum sample at 95% confidence interval is 111 young adults.