Sampling Calculation

A building firm called Jones and Son Ltd wish to carry out a survey of householders in Richmond upon Thames

William Jones has found out information from the 2011 census.
London Borough of Richmond upon Thames population: 191 400 (of which 93,000 are males). 

Housing status %	Richmond upon Thames %	England and Wales %
Owner occupier	85%	70%
Council tenant	5%	20%
Other	10%	10%

Age Group %	Richmond upon Thames %	England and Wales %
Under 16	20.8	20.2
16 - 17	5.2	4.9
18 - 29	13.1	12.6
30 - 59	39.0	41.5
60 and over	21.9	20.8

          The sample chosen is 18+ home owning males.

The firm has requested a stratified 3.5% sample of the target market. The criteria for the stratified sample is ‘Richmond borough male home owners over the age of 18’
Calculate:

1. The total sample size.

         2. State the number of males aged 18 – 29 in the sample.

         3. State the number of males aged 30 and over in the sample.

Show all your workings. 

Answer:
Population who are 18+ (13.1% + 39% + 21.9%) = 74%
93,000 (males) x 0.74 = 68,820
Home owning = 85%
68,820 x 0.85 = 58,497
3.5% sample:
58,497 x 0.035 = 2047.395
Sample size: Accept 2047 or 2048

Males who are 18 – 29:
2048 x 0.131 = 269
Males who are 30+ (39% + 21.9%) = 60.9%
2048 x 0.609 = 1248