A group of statistics students decided to conduct a survey at their university to find the average (mean) amount of time students spent studying per week. Assuming a population standard deviation of three hours, what is the required sample size if the error should be less than a half hour with a 99% level of confidence?

240

Formula:

n = [(z-value * sd)/E]^2

where n = sample size,

z-value will be 2.58 using a z-table to represent the 99% confidence interval

sd(standard deviation) = 3

E = 0.5

Substituting the parameters into the formula n = [(z-value * sd)/E]^2, we have,

n = [(2.58 ×3) ÷ 0.5]²

n = 239.63 approximately 240.

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