# A leading dental journal claims that 68% 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 ± 5%. What minimum sample size, rounded to the nearest whole person, does the hygienist need to use? Hint: ME equals plus or minus two times square root of start fraction p hat left parenthesis one minus p hat right parenthesis over N end fraction end square root, where p hat is the yes proportion in the sample and N is the sample size N ≥ 175 N ≥ 348 N ≥ 366 N ≥ 400

To calculate the minimum sample size needed to conduct a survey to verify the claim that 68% of young adults do not brush their teeth regularly.

The sample size for a proportion estimation is given by

where: is the z-score of the confidence level and p is the proportion being tested.

Setting our confidence level to be 95%, then = 1.96

Thus,

i.e. N ≥ 335.

Setting our confidence level to be 90%, then = 1.645

Thus,

i.e. N ≥ 236.

Setting our confidence level to be 99%, then = 2.58

Thus,

i.e. N ≥ 335.

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