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

unbiased estimate of

(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.