CAIE A-Level Mathematics A2 6.5.3 Mean Hypothesis Tests

[Maximum number: 5]

The numbers of green sweets in 200 randomly chosen packets of Frutos are summarised in the table.

Number of green sweets	0	1	2	3	>3
Number of packets	32	50	97	21	0

(a)

The manufacturers of Frutos claim that the mean number of green sweets in a packet is 1.65 .
Anji believes that the true value of the mean, $\mu$ , is less than 1.65 . She uses the results from the 200 randomly chosen packets to test the manufacturers' claim.

State suitable null and alternative hypotheses for the test.

[ 1 ]

$\mathrm{H}_{0}: \mu=1.65$ $\mathrm{H}_{1}: \mu<1.65$
Marking guidance:

Accept 'population mean' but not just 'mean'.

(b)

Show that the result of Anji's test is significant at the 5 % level but not at the 1 % level.

[ 4 ]

$\frac{{ }^{\prime} 1.535{ }^{\prime}-1.65}{\sqrt{0.783 \div 200}}$
Standardising with their mean.

=-1.838 or -1.84

A1*

$\Phi(0.05)$ and $\Phi(0.01)$ attempted
Or $\mathrm{P}\left(z<-{ }^{ˋ} 1.838 ˋ\right)$ attempted.

SC: Condone $\Phi(0.025)=2.807$ and $\Phi(0.005)=3.291$ following two-tailed test in (b).

-1.645>-1.838>-2.326

[Hence significant at 5\% but not 1\% level]
AG

=0.033 and 0.05>0.033>0.01

SC: use of 1.54 or 1.53 for the mean leading to -1.645>-1.758>- 2.326

or -1.645>-1.918>-2.326 or 0.95 < 0.9606 or 0.9724 < 0.99

scores M1 M1 A1.

Marking guidance:

Accept use of critical value method

1.535 < 1.547

or accept 1.65>1.638.

CAIE A-Level Mathematics A2 6.5.3 Hypothesis Tests Questions

Exam points

CAIE A-Level Mathematics A2 6.5.3 Hypothesis Tests Questions question 1

Question (a)

Question (b)