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MTHS4005 Coursework description
A company, Batmobile, manufacture’s batteries for mobile phones. Batmobiles standard battery, BMClassic, has been used in mobile phones for years and extensive data has been obtained concerning the usage hours between charge of a battery. Batmobile are planning to launch their new battery, TurboBM. Batmobile have asked you to analyse the data they have collected and to assess their claims concerning the TurboBM battery.
Batmobile batteries are used in mobiles produced by three different mobile phone manufacturers. For confidentially reasons these manufacturers are labelled A, B and C.
Batmobile have provided you with the following data in csv.files:
- Usage Data. The usage lifetime (minutes) of 168 TurboBM batteries in mobile devices produced by manufacturers A, B and C.
The usage lifetime is the total time a device is in use from fully charged to a flat battery (cannot be used) when used at a constant level of usage.
- Comparison Data. The usage lifetime of a TurboBM battery and a BMClassic battery on 66 days were recorded. Unfortunately the data were corrupted with some of the observations being lost and replaced by NAs.
- Laboratory Data 177 TurboBM batteries were tested under laboratory conditions to see how various factors affect the usage lifetime of the batteries. The covariates considered in the study were manufacturer (A, B, C), temperature oC, recharge, the number of times the battery had been recharged, memory, memory capacity of device (in GB) and level of usage (low, high)
Batmobile have asked for you to consider the following questions in preparing your report:
1. Using the Usage Data: Marks: 30
a) Provide an exploratory analysis of the Usage Data.
b) Construct a 92% confidence interval for the mean usage lifetime (minutes) for a TurboBM battery in a mobile device produced by manufacturer A.
c) Test whether or not a gamma distribution is appropriate for the usage lifetime (minutes) of a TurboBM battery in a mobile device produced by manufacturer C.
You may test whether a Gamma(21, 0.0556) distribution is appropriate, if you are unable to find an
appropriate gamma distribution to fit using the data.
2. Using the Comparison Data: Marks: 25
a) A visual summary of the data.
b) Is there correlation between the usage lifetime of a TurboBM and a BMClassic battery on a given day?
c) Is it reasonable to assume that the variance of the usage lifetime of TurboBM and BMClassic batteries is the same?
d) Is there evidence that the mean usage lifetime of a TurboBM battery is at least 60 minutes longer than the mean usage lifetime of a ClassicBM battery?
3. Using the Laboratory Data: Marks: 25
a) Explore the relationship between usage lifetime and temperature. If appropriate, consider including a transformation of temperature in your model.
b) Fit a linear model to the usage lifetime.
c) Choose the most appropriate linear model for the data.
d) Comment on the model fit and affect of the selected covariates on the usage lifetime.
e) Choosing an appropriate model, provide a 75% prediction interval for the usage lifetime of a TurboBM battery which has been recharged 68 times in a manufacturer B device with memory 256GB, with High usage at temperature -0.5oC.