What is stratified sampling? Why would it be used?
A local authority official wishes to conduct a survey of households in the borough. He decides to select a stratified sample of 2000 households using Council Tax property bands as the strata. At the time of the survey there are 79368 households in the borough. The table shows the numbers of households in the different tax bands.
Tax band
A - B
C - D
E - F
G - H
Number of households
32298
33211
9739
4120
Calculate the number of households that the official should choose from each stratum in order to obtain his sample of 2000 households so that each stratum is represented proportionally.
What assumption needs to be made when using a Wilcoxon single sample test?
As part of an investigation into trends in local authority spending, one of the categories of expenditure considered was 'Highways and the Environment'. For a random sample of 10 local authorities, the percentages of their total expenditure spent on Highways and the Environment in 1999 and then in 2009 are shown in the table.
Local authority
A
B
C
D
E
F
G
H
I
J
1999
9.60
8.40
8.67
9.32
9.89
9.35
7.91
8.08
9.61
8.55
2009
8.94
8.42
7.87
8.41
10.17
10.11
8.31
9.76
9.54
9.67
Use a Wilcoxon test, with a significance level of \(10 \%\), to determine whether there appears to be any change to the average percentage of total expenditure spent on Highways and the Environment between 1999 and 2009.