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Assignment 3 X3.8 (vi)

A

amyb45

Member
I am wondering if someone can help me with this question - I'm not sure what I'm supposed to use or look at in order to tell whether the long-life battery lasts 3 times longer than the standard battery. I assume I need to compare some of the statistics calculated in the question but I'm not sure how.

Any help would be appreciated. Thanks in advance.
 
Looks like a one sided confidence interval question. You need an assumed distribution for battery life then you want the prob that long life > 3* ordinary at a high percentage level eg 95%.
 
Is my assumed distibution binomial which can then be approximated by a normal ? Does the probability need to be calculated at each different interval for t?
 
The assertion is that the special battery lasts 3 times as long. So, what we should be doing is looking at F(t) for the ordinary battery and comparing this with F(3t) in the special battery. These numbers should be broadly similar for the assertion to be true.

I agree with bystander that some sort of confidence interval is needed to officially test this but we do not have enough data to do so.

In a situation like this in the exam, it is best to give as much evidence from the data as you can that is relevant to either confirming or denying the assertion.

Good luck!
John
 
I was thinking about this and also about a similar question 3.15 part ii) in the Q&A bank.

Can we use the same logic as with the trapezium rule to carry out a statistical test on all of these time intervals [which sum up to a year]? the weights could be the appropriate time intervals - e.g. 5/12 for 5 months (6< t<11), 3/12 for 3 months and so on..
Under the UDD assumption, could this be a valid approach?
 
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I'm not convinced by this. It's certainly not an approach that I've seen taken by the examiners.

I agree with John, that if some sort of calculation/statistics were required (rather than just a comment), a confidence interval approach would be the way to go.
 
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