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Paper 1 – Confidence Intervals

Example

The noon temperature , in degree Celsius , in a city through the year is studied . A sample of 10 observations is recorded on 10 different days , recorded as below :

18.5 , 19.4 , 20.1 , 22.3 , 19.5 , 24.1 , 23.4 , 17.9 , 21.5 , 23.3

( a ) Find an unbiased estimate of the population mean . [ 2 ]

( b ) Find sn _� 1. [ 2 ]

( c ) Construct a 95 % confidence interval for the population mean , giving the answer to three decimal places .

[ 2 ]

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Solution

( a ) An unbiased estimate 18.5 �19.4 � � 23.3

� ( A1 ) for correct approach 10

( b )

� 21 C A1 sn _� 1

�

( 18.5 � 21 ) � ( 19.4 � 21 ) � � ( 23.3�

21 ) 10 �1 sn _� 1

� 2.213092356 C

2 2

2 sn _� 1

� 2.21 C A1

( c ) 95 % confidence interval : ( 19.417 , 22.583 ) A2

( A1 ) for correct approach

[ 2 ]

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