User interface language: English | Español

Date May Example question Marks available 3 Reference code EXM.1.AHL.TZ0.59
Level Additional Higher Level Paper Paper 1 Time zone Time zone 0
Command term Calculate Question number 59 Adapted from N/A

Question

The heights, x metres, of the 241 new entrants to a men’s college were measured and the following statistics calculated.

x = 412.11 , x 2 = 705.5721

The Head of Mathematics decided to use a χ 2  test to determine whether or not these heights could be modelled by a normal distribution. He therefore divided the data into classes as follows.

Calculate unbiased estimates of the population mean and the population variance.

[3]
a.

State suitable hypotheses.

[1]
b.i.

Calculate the value of the χ 2  statistic and state your conclusion using a 10% level of significance.

[11]
b.ii.

Markscheme

x ¯ = 412.11 241 = 1.71             A1

s 2 = 705.5721 240 412.11 2 240 × 241 = 0.0036         M1A1

[3 marks]

a.

H0: Data can be modelled by a normal distribution

H1: Data cannot be modelled by a normal distribution           A1

[1 mark]

b.i.

The expected frequencies are

       A1A1A1A1A1A1

χ 2 = 5 2 8.04 + 34 2 30.19 + + 12 2 16.10 241 = 3.30 / 3.29        M1A1

Degrees of freedom = 3       A1

Critical value = 6.251 or p-value = 0.35       A1

The data can be modelled by a normal distribution.       R1

[11 marks]

b.ii.

Examiners report

[N/A]
a.
[N/A]
b.i.
[N/A]
b.ii.

Syllabus sections

Topic 4—Statistics and probability » SL 4.9—Normal distribution and calculations
Show 181 related questions
Topic 4—Statistics and probability » SL 4.11—Expected, observed, hypotheses, chi squared, gof, t-test
Topic 4—Statistics and probability » AHL 4.12—Data collection, reliability and validity tests
Topic 4—Statistics and probability » AHL 4.14—Linear transformation of a single RV, E(X) and VAR(X), unbiased estimators
Topic 4—Statistics and probability

View options