Further Mathematics · Pearson Edexcel 9FM0 · Option FS2 · Topic 6

Other hypothesis tests and confidence intervals

Tests and confidence intervals for a normal variance, and the F-test for comparing two variances.

2 sub-topics
Taught in Year 13
30 practice questions
2 animated lessons

Practice questions (30) Lessons Worksheets All Edexcel Further Mathematics topics

What the specification says

Every sub-topic Pearson Edexcel can examine in this topic, with its reference number from the official specification. The Y12 and Y13 tags show when each sub-topic is usually taught.

6.1Tests and intervals for a normal varianceY13
6.2F-test for equality of variancesY13

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Easy, medium and hard questions from this topic, each with a worked solutions and the mark for every step. All 30 questions in this topic, free, no account needed.

Other hypothesis tests and confidence intervals

Not needed for Year 12Easy

What the F-test assumes · Year 13 · 1 mark

Which assumption does the F-test for equal variances need?
(1)

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The test is sensitive to the Normal assumption. $D$ : Both samples are random and independent, from Normal populations

Total1

MMethod mark: for a correct method, even with a slip.
AAccuracy mark: for a correct answer from a correct method.
BIndependent mark: for a correct fact or result on its own, with no method needed.

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Other hypothesis tests and confidence intervals

Not needed for Year 12Medium

The distribution for a Normal variance · Year 13 · 1 mark

A random sample of size $n$ from a Normal population has unbiased variance estimate $S^{2}$ . Which statistic has a chi-squared distribution with $n - 1$ degrees of freedom?
(1)

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It is used for confidence intervals and tests for $\sigma^2$ .A: $\dfrac{(n - 1)S^2}{\sigma^2}$

Total1

MMethod mark: for a correct method, even with a slip.
AAccuracy mark: for a correct answer from a correct method.
BIndependent mark: for a correct fact or result on its own, with no method needed.

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Other hypothesis tests and confidence intervals

Not needed for Year 12Hard

A test for a normal variance · Year 13 · 5 marks

The lengths of rods are normally distributed, with variance 4 mm² when the machine is working correctly. A random sample of 15 rods has unbiased variance estimate 6.4 mm².

Test, at the 5% level, whether the variance has increased.
(5)

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$H_0: \sigma^2$ ${}= 4, \ H_1: \sigma^2 > 4$
This has $a \chi^{2}$ distribution with $n - 1$ degrees of freedom. $\frac{(n - 1)S^2}{\sigma^2}$ ${}= \frac{14 \times 6.4}{4}$ ${}= 22.400$
$\chi^2_{14}: \ \text{cv} = 23.685$
Do not reject H₀: there is insufficient evidence that the variance has increased.

Total5

MMethod mark: for a correct method, even with a slip.
AAccuracy mark: for a correct answer from a correct method.
BIndependent mark: for a correct fact or result on its own, with no method needed.

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