3. In 2014, due to the drought, the California State Water Resources Control Boa

Question

3. In 2014, due to the drought, the California State Water Resources Control Board approved emergency regulations that allowed local law enforcement and water agencies to impose a maximum S500-a-day fine on water wasters. A city with 4380 households is interested to know what percent of its households would be subject to the fine. To sample using k 20 of water agency accounts and determine whether the usage would correspond to a fine. (Assume that each household has a unique water agency account, and that account numbers are randomly assigned.) They find that 30 of the sampled households would be fined. Estimate the proportion of households in the city that would be fined, and give a standard error for your estimate. Do you think this standard error wil be about right, an overestimate, or an underestimate?

Explanation / Answer

Here number of samples, n = N/k = 4380 / 20 = 219

proportion of households that would be subject to the fine 'p' = 30/219 = 0.137

standard error of 'p' = sqrt(pq/n) = sqrt(0.137 * 0.863/219) = 0.023

It will be right since it is < 0.05

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