Q.5 - The Practice of Statistics for AP

Question

1) State whether it is a parameter or a statistic and (2)use appropriate notation to describe each

 number; for example, p = 0.65. 

 Get your bearings A large container of ball bearings has mean diameter 2.5003 centimeters (cm). This is within the specifications for acceptance of the container by the purchaser. By chance, an inspector chooses 100 bearings from the container that have a mean diameter of 2.5009 cm. Because this is outside the                      

Step-by-Step Solution

Answer

1)The given statement is a parameter

2)The notation of the population mean is $2.5003$  and the notation of sample mean is $\overline{x}=2.5009$  

       

Part (1) Step 1: Given Information

Mean diameter of the container centimeters =2.5003

Mean diameter of the 100 bearings $=2.5009$ centimeters

Part (1) Step 2: Explanation

A parameter is an expressive measure for a population, as we all know. A statistic is also a term for an expressive measure for a sample.

The mean diameter of the large container serves as an expressive measure for a population in this case. This implies that it is neither a statistic nor a parameter.

Also, the population means is,$\mu =2.5003$$\mu =2.5003$.

Part (2) Step 1: Given Information

Mean diameter of the container $=2.5003$ centimeters

Mean diameter of the 100 bearings $=2.5009$ centimeters

Part (2) Step 2: Explanation

A parameter is an expressive measure for a population, as we all know. A statistic is also a term for an expressive measure for a sample.

The average diameter of 100 bearings from the large container is used as an expressive metric for a sample in this case.

Also, the sample mean is, $\overline{x}=2.5009$ and the population mean is, $\mu =2.5003$.