Question

Bearings A production run of ball bearings is supposed to have a mean diameter of $2.5000$centimeters (cm). An inspector chooses $100$bearings at random from the run. These bearings have mean diameter $2.5009$cm.

identify the population, the parameter, the sample, and the statistic.

Short answer

The sample is of $100$bearings and population mean diameter becomes the associated parameter. The parameter is population mean diameter $\mathrm{\mu }$and statistic is sample mean diameter $\overline{\mathrm{x}}=2.5009\mathrm{cm}$.

Step-by-step solution

Given information

We need to identify the population, the parameter, the sample, and the statistic.

Simplify

Individuals that seek to collect information are present in the population.

A sample is a portion of the population from whom data was gathered.

It is noted that the sample consists of $100$bearings randomly chosen from the run, whereas the population must consist of all bearings in the run.

A statistic is a descriptive measure for a sample, whereas a parameter is a descriptive measure for a population.

The mean diameter of $2.5009\mathrm{cm}$is calculated based on $100$bearings in the sample, hence $2.5009\mathrm{cm}$reflects the sample mean diameter, which means $2.5009\mathrm{cm}$is a statistic.

The population mean diameter becomes the associated parameter.

Statistic :

$\overline{x}=$sample mean diameter $=2.5009\mathrm{cm}$
Parameter : $\mu =$population mean diameter