A factory makes candles of a particular type. Each day the candles are made in 11 batches, numbered 2 to 12. Ravi, the quality manager, chooses one batch each day for checking. He throws two fair six-sided dice and chooses the batch whose number is the total of the two scores.
(a) Show that this method of choosing a batch is not random.
(2 marks)
To check the burning time of a candle, the candle is lit and left to burn until it goes out.
(b) State one reason why Ravi tests a sample of candles rather than every candle that is made.
(1 mark)
In the past the burning times of candles of this type had mean 32.5 hours. The factory has recently changed to a cheaper wax, and Ravi wishes to test whether the mean burning time has decreased. He now uses a correct method to choose a random sample of 45 candles made with the cheaper wax, and finds that their mean burning time is 31.9 hours. It is given that the standard deviation of the burning times is 2.2 hours.
(c) Carry out the test at the 1% significance level.
(7 marks)
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