2013 A-level H2 Mathematics (9740) Paper 2 Question 9 Suggested Solutions

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions.

9
(i)
From the graphing calculator,

unbiased estimate of population mean

unbiased estimate of population variance

(ii)
We assume that 2.31 is a good estimate of the unknown population variance.
We assume the distance travelled per litre of fuel by a car is independent of another car.

Under , perform a left-tailed T-test.

Test statistic,

Using the graphing calculator, p-value , thus we do not reject .

There is insufficient evidence at 5% significance level to say that the distance travelled per litre of fuel is too high.

KS Comments:

This is a fairly manageable question that should be attempted. The only issue is probably with the assumption part. Students cannot use their regular “assume population mean followed a normal distribution” assumption since the question stated it. So they need to be more creative. As to what constitutes a good estimate, we consider if they are consistent and unbiased.