Hint
State whether the population variance is known. Multiply the standard error by the two-sided critical z.
Worked solution
(a)
\(\displaystyle h= \frac{1.9599639845(3)}{\sqrt{25}}= 1.17597839072403\)
Answer: \(1.17597839072403\).
Answer: \(\approx 1.17597839072403\)
(b)
\(45-1.175978391=43.824021609276\)
Answer: \(43.824021609276\).
Answer: \(\approx 43.824021609276\)
(c)
\(45+1.175978391=46.175978390724\)
Answer: \(46.175978390724\).
Answer: \(\approx 46.175978390724\)
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.