Your Practice Paper – Applications and Interpretation HL for IBDP Mathematics SE Production Limited 32 � Properties of point estimation : 1 . 2 2 1 1 ( ) 1 n i i n X X s n � � � � � � : Sample variance 2 . 2 2 1 ( ) n i i n X X s n � � � � 3 . 2 2 1 1 n n n s s n � � � 4 . E ( ) X X � 5 . 2 2 1 E ( ) n s � � � � ( 1 )% � � confidence interval for population mean � when the population variance 2 � is known : 1 . 1 2 n X X X X n � � � � : Sample mean 2 . 2 2 , X z X z n n � � � � � � � � � � � � � � , where 2 2 P Z z � � � � � � � � � � 3 . 2 2z n � � � : Interval width � ( 1 )% � � confidence interval for population mean � when the population variance 2 � is unknown : 1 . 1 2 n X X X X n � � � � : Sample mean 2 . 1 1 1 , 1 , 2 2 , n n n n s s X t X t n n � � � � � � � � � � � � � � � � , where 1 , 2 2 n P X t � � � � � � � � � � � 3 . 1 1 , 2 2 n n s t n � � � � : Interval width 30 Interval Estimation