College statistics (Provided Question in Description Box)

Question

Local health authorities are concerned that the hectic pace in their city has elevated the stress, and thus the blood pressure of women. The authorities have decided to study this issue by measuring the blood pressure of a random sample of patients in the city over the next year and estimating the mean blood pressure, , of women in the city. Blood pressure is approximately normally distributed in humans, and a 15-year-old study suggests the standard deviation of women's blood pressure is about 8 mm Hg. Suppose the health authorities accept this value as a reasonable estimate of the standard deviation of blood pressure of today's women in this city. If it is desired to estimate to within 1.0 mm Hg with 95% confidence, what sample size is necessary

Answer 1

Confidence interval = standard error of the mean * z-score of the interval

= standard deviaton/ sqrt(n) * z-score(95% CI)

= 8/sqrt(n) * 1.96

=15.68/sqrt(n)

We want our interval to be no more than 1 mm away from the mean so we can setup an inequality.

 

15.68/sqrt(n) <= 1

15.68 <= sqrt(n)

15.68^2 < = n

245.86 <= n

 

Since you can't sample fractional people, the most amount of people you could sample and guarantee a confidence interval of within 1 mm of the mean is 245.