Question

A study on students drinking habits wants to determine the true average number of alcoholic drinks all FSU graduate students have in a one week period. We know from preliminary studies that the standard deviation is around 1.79. How many students should be sampled to be within 0.5 drinks of population mean with 95% probability?

A. 50
B. 49
C. 24
D. 25

Answer 1

To determine the sample size needed to estimate the population mean with a certain level of confidence and precision, we can use the formula:

n = ((z * σ) / E)^2

where:
- n is the sample size
- z is the z-score corresponding to the desired level of confidence (95% confidence corresponds to a z-score of 1.96)
- σ is the standard deviation of the population
- E is the margin of error (half the width of the confidence interval, which in this case is 0.5)

Plugging in the given values, we get:

n = ((1.96 * 1.79) / 0.5)^2
n = 48.93

Rounding up to the nearest whole number, we get:

n = 49

Therefore, the answer is B. 49 students should be sampled to be within 0.5 drinks of the population mean with 95% probability.