Sample sizes using statistics (MR, unit 9)

Can only be used for probability samples.

Need 3 pieces of information:

• O = estimate of standard deviation of population
• Z = level of confidence expressed in standard errors
• R = acceptable level of precision (the sampling error)

N = sample size
SE = standard error of the mean

MEASURING AVERAGES

N = (Z * O /R)2

sample size = (2.58*£50/£10)2

This is just using algebra to calculate n in the equation to find the standard error.

Example: We estimate average salary to be £20,000 with a standard deviation of £50. What size of sample should be taken to estimate the true average salary to within £10, with 99% confidence?£10 = 2.58*£50/ route sample size
n = (2.58*50/10)2
n = 166.41 (round up to 167)
A samples size of 167 needed to estimate the true average income to within £10 and be 99% confident of our answer.

MEASURING PROPORTIONS

N = Z2 * PQ / R2

How many people should be sampled to be 99% confident of the number of people likely to take up offer within 0.5% of the population?
P = 20% 0.2
R = 0.5% 0.005

n = 2.58(2) * 0.2 * (1-0.2) / 0.005(2)
n = 5,219