Quick questions on Linear combinations and statistical inference: VCE Specialist Mathematics Unit 4

4short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What is wrong tail for the

p

value?

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A one-sided test uses one tail; a two-sided test doubles the tail probability. Match the

p

value to the alternative hypothesis.

What is q1?

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X

and

Y

are independent with

\mathrm{Var}(X) = 5

\mathrm{Var}(Y) = 3

. Find

\mathrm{Var}(X - Y)

. [2 marks]

What is q2?

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A sample of

n = 36

from a population with

\sigma = 12

has mean

\bar{x} = 70

. State the standard error of the mean. [1 mark]

What is q3?

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For a test of

H_0: \mu = 100

against

H_1: \mu \neq 100

, the test statistic is

z = 2

. State the

p

value. [2 marks]

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