Assignment 3 X3.8 (vi)

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?

 

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?

 

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.