A manufacturer has tested 11 lithium-ion batteries, and finds that their lifetime is 400 charge cycles with a standard deviation of 10. An engineer is testing a cheaper design and wants to know if it has changed battery life. The average lifetime for 10 of the new batteries is 390 cycles, and the standard deviation of that sample is 8. Define change in lifetime as New minus Old. What is the best estimate of the change in lifetime

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Step-by-step explanation:

Hello!

You have two samples and measured the lifetime of the batteries:

X₁: "Lifetime of a lithium battery from the old design"

n₁ = 11 lithium batteries

x[bar]₁ = 400 charge cycles

S₁ = 10 charge cycles

X₂: "Lifetime of a lithium battery from the new design"

n₂ = 10 lithium batteries

x[bar]₂ = 390 charge cycles

S₂ = 8 charge cycles

You need to estimate the difference in the lifetime as New minus Old, I already defined both variables separately, so the difference is:

X₂-X₁

The best way to compare both samples and tests if I change the life of the batteries is through their means. So the best estimate for the change in the lifetime of the lithium batteries is:

x[bar]₂-x[bar]₁

Calculate the difference as ⇒ 390 - 400 = - 10 life cycles.

Since it's a negative number it looks like this estimation doesn't have any sense. It is common for estimates to take values that do not follow common sense. Think that mathematically this value does make sense, and in this case, the negative number indicates the direction in which these populations tend. If you did a statistical test, you may come to the conclusion that, in general, the new battery design has a shorter lifespan than the old battery design.

I hope you have a SUPER day!