Business Statistics - QBM117 Revising interval estimation

Objective w To develop confidence in identifying the correct formula to use when calculating an interval estimate.

Identifying the parameter to be estimated w In this subject we need only concern ourselves with estimating the population mean , or the population proportion p. w Generally it is clear from the question, which parameter we are estimating, if we read it carefully enough.

Two confidence interval estimators of  w If  is known, the confidence interval estimator of the population mean  is There are two different interval estimators of the population mean, and the basis for determining which method is appropriate is quite simple. w If  is unknown and the population is normally distributed, the confidence interval estimator of the population mean  is When d.f > 200 we approximate t by thevalue.

Only one confidence interval estimator of p w There are is only one confidence interval estimator of the population proportion so there is no choice. w One condition however must be satisfied before it is appropriate to use this formula

Example 1 Do we know the population standard deviation,  or do we only have the sample standard deviation s? mean Does the question ask us to estimate a mean or a proportion? S

The average assembly time is between secs and secs

C.C. Therefore 166 times should be sampled.

Example 2 Do we know the population standard deviation,  or do we only have the sample standard deviation s? mean Does the question ask us to estimate a mean or a proportion? 

The average daily income is between $ and $

C.C. Therefore 353 businesses should be sampled.

Example 3 proportion Does the question ask us to estimate a mean or a proportion?

The proportion of depositors with both types of accounts is between 93.5% and 99.7%

C.C. Therefore 552 customers should be sampled.

Reading for next lecture Chapter 10 Sections