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 \mu = 12.8

unbiased estimate of {\sigma}^{2} = 2.31

(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.

H_0: \mu = 13.8
H_1: \mu < 13.8 Under H_0, perform a left-tailed T-test.

Test statistic, T ~ = ~ \frac{\bar{X}-\mu}{\frac{s}{\sqrt{n}}} ~ \sim ~ t(7)

Using the graphing calculator, p-value = 0.052397 > 0.05, thus we do not reject H_0.

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.

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