Question

An electronics store receives a shipment of eight boxes of calculators, with ten calculators in each box. A quality control inspector chooses a box by putting eight identical slips of paper numbered 1 to 8 into a hat and picking a slip at random. He then chooses a calculator at random from the box selected using a similar method with ten slips of paper in a hat. He repeats the process until he obtains a sample of 5 calculators for quality control testing. Does this sampling plan result in a simple random sample? Explain.

Answer 1

Yes

Explanation:

If you take the number of calculators that needed to be checked, the inspector made it random by adding the slips of paper into a hat for selecting the boxes. The chances of any of the calculators to be selected are also equal as he used the same process again to select a certain calculator in the different boxes. This is actually a great example for a simple random sample.

Answer 2

Yes, this sampling plan will result in a simple random sample.

Explanation:

Given is that -

The inspector chooses a box by putting eight identical slips of paper numbered 1 to 8 into a hat and picking a slip at random. This way ensures that any box will be chosen.

He then chooses a calculator at random from the box selected using a similar method with ten slips of paper in a hat. This way ensures that any calculator can be chosen.

We can see that the sample is RANDOM as all calculators have the same chance of being chosen. It is also a simple random sample as all samples of 5 calculators have the same chance of being chosen.