Rice survey

p = 17/36 = 0.472   use 'Old' varieties

Use this diagram to explain that the distributions of the count of successes, proportion of successes and estimation error all have distributions with the same shape but different scaling.

(Note that the sample proportion, p, is used instead of the unknown π to draw the distributions and evaluate the se.)

Mention that the error distribution is particularly important — its standard deviation is the standard error.

We estimated that a proportion 0.472 of farmers in the region use 'Old' varieties. From the error distribution, it is unlikely that this estimate will be in error by more than 0.2.


As part of a survey of rice producers in Sri Lanka, 36 farmers were randomly selected from 4 villages. Each sampled farmer was asked about the variety of rice that he used and the varieties were categorised as 'Old', 'Traditional' or 'New'. The 36 categorical values are described by the following frequency table.

Old varieties    17
Traditional varieties    15
New varieties 4
Total farmers    36