Point Estimation problem Please explain in clear handwriting and I\'ll rate Powe

Question

Point Estimation problem

Please explain in clear handwriting and I'll rate

Power outages during winter storms is common. A utility company which
provides electricity to Pacific Northwest wants to estimate the true proportion of
outages that affect an area large enough (denoted as class A) that will take longer
than 24 hours to restore electricity. The company collects some data over three
winters for 365 outages. 62 outages are recorded as class A. We would like to
assess the properties (Bias, Variance, MSE) of the estimator of the true population
proportion of class A outages. First state your estimator. Then state either an
analytical result or a stepwise simulation procedure to assess the properties of this
estimator.

Explanation / Answer

The estimator used in this scenario is the Population Proportion. That is the proportion of outages rated as A, the ones that tae longer thn 24 hours to restore electricity

.

So in this scenario a sample of 365 outages has been observed. This is an observtaional study

it is noted that 62 outages are marked as A

this implies the proportion of outages marked as A are : 62/365

Thus the best estimate of population proportion is the sample proportion P^ = 62/365

Population proportion is denoted by P

It is estimated by the sample proportion P^ = 62/365

.

The bias for this estimate is : P^-P

.

The variance would be: p^*q^/n

.

Mean Standard error is given by the formula: E = Z * sqrt(p^*q^/n)

.

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