- The average time it takes for a new kettle to boil, when full of water, is 305 seconds. An old kettle will take longer, on average, to boil. Alun suspects that a particular kettle is an old kettle. He boils the full kettle on 9 occasions and the times taken, in seconds, are shown below.
305
295
310
310
315
307
300
311
306
You may assume the times taken to boil the full kettle are normally distributed.
- Calculate unbiased estimates for the mean and variance of the times taken to boil the full kettle.
- Test, at the \(5 \%\) level of significance, whether there is evidence to suggest that this is an old kettle.
- State a factor that Alun should control when carrying out this investigation.