Question

A study on students drinking habits wants to determine the true average number of alcoholic drinks all UF "greek" students have in a one week! period. We know from preliminary studies that the standard deviation is around 6.3. How many students should be sampled to be within 0.5 drink! of population mean with 95% probability?

A. 609 B. 305 C. 304 D. 610

Answer 1

Explanation:

We can use the formula for the sample size required to estimate the population mean with a given margin of error and confidence level:

n = (z^2 * s^2) / E^2

Where:

z = the z-score associated with the desired confidence level (95% confidence level corresponds to z = 1.96)

s = the known standard deviation of the population

E = the desired margin of error

Plugging in the given values, we get:

n = (1.96^2 * 6.3^2) / 0.5^2

n = 609.45

Rounding up to the nearest whole number, we get that a sample size of 610 students is required to estimate the true average number of drinks within 0.5 with 95% probability. Therefore, the answer is option D.