Hint
Use independent random observations. Divide the observation sum by n.
Worked solution
(a)
\(\displaystyle \bar{x}= \frac{320}{16}= 20\)
Answer: \(20\).
Answer: \(20\)
(b)
\(\displaystyle s^{2}= \frac{6505- \frac{320^{2}}{16}}{16- 1}= 7\)
Answer: \(7\).
Answer: \(7\)
(c)
\(\displaystyle \sqrt{\frac{7}{16}}= 0.661437827766148\)
Answer: \(0.661437827766148\).
Answer: \(\approx 0.661437827766148\)
Maths4U indicative marking guidance
Maths4U indicative marking guidance, not an official mark scheme. Credit valid alternative reasoning and consequential working; do not award a reasoning mark for an unexplained final answer.
(a) · 2 marks
- 1 mark: Divide the observation sum by n.
- 1 mark: Obtain the stated result with the required sign, units and domain.
Alternative methods: Any complete mathematically valid method with the stated assumptions and equivalent result is acceptable.
Common error: Do not report the sample standard deviation as the standard error.
(b) · 2 marks
- 1 mark: Correct the centred sum of squares with n−1.
- 1 mark: Obtain the stated result with the required sign, units and domain.
Alternative methods: Any complete mathematically valid method with the stated assumptions and equivalent result is acceptable.
Common error: Increasing n reduces the uncertainty of the mean, not the population variance.
(c) · 2 marks
- 1 mark: Divide the sample standard deviation by \(\displaystyle \sqrt{n}\).
- 1 mark: Obtain the stated result with the required sign, units and domain.
Alternative methods: Any complete mathematically valid method with the stated assumptions and equivalent result is acceptable.
Common error: Do not report the sample standard deviation as the standard error.
Total: 6 marks.