Moderate -0.8 This is a straightforward confidence interval calculation requiring only the standard formula with a normal distribution (large sample). Students need to recall z* = 2.17 for 97% confidence and apply CI = x̄ ± z*(σ/√n). It's routine application with no conceptual challenges or problem-solving required, making it easier than average.
Murni is investigating the annual salary of people from a particular town.
She takes a random sample of 200 people from the town and records their annual salary.
The mean annual salary is £28 500 and the standard deviation is £5100
Calculate a 97% confidence interval for the population mean of annual salaries for the people who live in the town, giving your values to the nearest pound.
[3 marks]
Question 4:
4 | Obtains correct z-value
AWRT 2.17
PI by a correct upper or lower limit
of the confidence interval. | 1.1a | B1 | z = 2.17
s2
x±z
n
5100
= 28500±2.17×
200
= (27 717, 29 283)
Uses formula for upper or lower
limit of a confidence interval using
their z-value.
Condone use of 5100
Condone use of t-value. | 1.1a | M1
Obtains the correct confidence
interval.
CAO | 1.1b | A1
Total | 3
Q | Marking Instructions | AO | Marks | Typical Solution
Murni is investigating the annual salary of people from a particular town.
She takes a random sample of 200 people from the town and records their annual salary.
The mean annual salary is £28 500 and the standard deviation is £5100
Calculate a 97% confidence interval for the population mean of annual salaries for the people who live in the town, giving your values to the nearest pound.
[3 marks]
\hfill \mbox{\textit{AQA Further AS Paper 2 Statistics 2020 Q4 [3]}}