Question

Rudy Researcher is now interested in the drinking habits of students at the University of Alabama. It is known that the average yearly consumptions of soft drinks by college students nationwide is 50 gallons (µ = 50) with a standard deviation of 3.5 gallons (σ = 3.5). To minimize costs, the Committee would like to reduce that 95% confidence interval to have a width of 0.5 gallons. What sample size would they need to collect in order to reduce their error to 0.5 (E = 0.5)?

Answer 1

Solution :

Given that,

Population standard deviation = = 3.5

Margin of error = E = 0.5

At 95% confidence level the z is,

= 1 - 95%

= 1 - 0.95 = 0.05

/2 = 0.025

Z_/2 = Z _0.025 = 1.96

sample size = n = [Z_/2* / E] ²

n = [1.96 *3.5 / 0.5 ]²

n = 188.23

Sample size = n = 189