All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions.
From the graphing calculator,
unbiased estimate of population mean
unbiased estimate of population variance
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.
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.
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.