Hint
State whether the population variance is known. Multiply the standard error by the two-sided critical z.
Worked solution
(a)
\(\displaystyle h= \frac{1.9599639845(4)}{\sqrt{36}}= 1.30664265636004\)
Answer: \(1.30664265636004\).
Answer: \(\approx 1.30664265636004\)
(b)
\(46-1.306642656=44.69335734364\)
Answer: \(44.69335734364\).
Answer: \(\approx 44.69335734364\)
(c)
\(46+1.306642656=47.30664265636\)
Answer: \(47.30664265636\).
Answer: \(\approx 47.30664265636\)
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: Multiply the standard error by the two-sided critical z.
- 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 use z(1−α) for a two-sided 1−α interval.
(b) · 2 marks
- 1 mark: Subtract the margin of error from the sample mean.
- 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: Round a required sample size up, not to the nearest integer.
(c) · 2 marks
- 1 mark: Add the margin of error to the sample mean.
- 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 use z(1−α) for a two-sided 1−α interval.
Total: 6 marks.