Question

you are receiving a large shipment of batteries and want to test their lifetimes. explain why you would want to test a sample of batteries rather than the entire population.

choose the correct answer below.

a. the percentage of defective batteries can change in the time it takes you to test all the batteries.
b. if you test all the batteries to failure you would have no batteries to sell.
c. if you test all the batteries you cannot form any conclusions about the population.

Explanation:

⚡ Using what you learned: Population vs. Sample

Step 1: Analyze the nature of the test

Testing the lifetime of a battery requires running the battery until it completely runs out of power (testing to failure). This is a destructive test because the item being tested is destroyed or rendered useless in the process.

Step 2: Evaluate the options

• A. The percentage of defective batteries can change in the time it takes you to test all the batteries.

While time-consuming, this is not the primary logical constraint preventing a full population test.

• B. If you test all the batteries to failure you would have no batteries to sell.

Because testing a battery's lifetime destroys its utility, testing the entire population would leave you with zero working inventory. Therefore, you must test a representative sample instead.

• C. If you test all the batteries you cannot form any conclusions about the population.

This is incorrect; testing the entire population would give you exact data about it, but it is practically impossible here due to the destruction of the product.

Answer:

B. If you test all the batteries to failure you would have no batteries to sell