Question

Discuss a real life problem that is solved with the Sufficiency Principle of data reduction by elaborating on the following:.

1. State the real-life problem.

2. Formulate the problem by giving a distribution for a sample in a real-life situation.

3. Find a sufficient statistic based on the sample.

4. Discuss how the statistic is used as a data reduction device in the rea life problem.

Answer 1

1. Suppose, a new Internet Service Provider estimate average monthly consumption of data (in gb) on regular basis for its current customer base so that he can design data plan accordingly. For the same, he randomly chooses the 1000 households from target area and recorded their data usage per month.
2. Without loss of generality, assume that, the data usage of customer in a month (X) follows normal distribution with mean µ and variance σ² which is unknown.
3. The sufficient statistic for estimating mean data consumption (µ) is sample mean consumption based on the 1000 data points of collected data.
4. Note that, the sample mean contains all the information that the sample – {X1, X2, . . . , X1000} has to offer regarding population mean consumption of data (µ). Thus, for estimating the population mean, it is enough to know (and store in record) mere value of instead of keeping record of all the samples for each month. This is how data reduction is achieved using sufficiency principle.