Estimation, confidence intervals and tests — WST03 IAL Further Mathematics practice questions · Study-IAL

Estimation, confidence intervals and tests

WST03Topic 3.33 questions

Unbiased estimators, the Central Limit Theorem, confidence intervals and tests for means.

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3974840−40×432

s^2 = \dfrac{880}{39} = 22.6

(3 s.f.) (1)

43 \pm 1.96 \times \sqrt{\dfrac{22.56\ldots}{40}}

(1)

(41.53,\ 44.47)

(1)

A

=

μ_{B}

H_0: \mu_A = \mu_B

H_{0} : μ_{A} = μ_{B}

H_1: \mu_A > \mu_B

M1 Standard error

\sqrt{\dfrac{16}{50} + \dfrac{25}{60}}

(1)

z = \dfrac{23.1 - 21.6}{\sqrt{0.7367}}

(1)

z = 1.75

(awrt) (1)

B1 Critical value

1.6449

(or

p = 0.040 < 0.05

) (1)

A1 Reject

H_0

: there is evidence that brand A batteries last longer on average (1)