Apps. and Interpretation for IBDP Maths Ebook 2 | Page 291

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Paper 1 – Z-Test
Example
The lengths of pencils produced in a factory is studied . It is given that the population standard deviation of the length is 0.1 cm . 50 pencils are randomly selected to form a sample such that the sample mean is 15.05 cm . Norman claims that the population mean
� is greater than 15 cm .
A hypothesis test is conducted at a 5 % significance level to test Norman ’ s claim .
( a ) ( i ) Write down the null hypothesis of the test .
( ii )
Write down the alternative hypothesis of the test .
( b )
Find the p -value.
( c )
State the conclusion of the test with a reason .
Solution
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( a ) ( i ) H
0
: � � 15 A1
( ii ) H
1
: � � 15 A1
( b ) p-value � 0.0002035177224 ( A1 ) for correct value p-value � 0.000204 A1
( c )
The null hypothesis is rejected .
A1
As p-value � 0.05
.
A1
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