Exercise 71
1 . The Body Mass Index ( BMI ) of a group of patients in a ward is studied . 8 patients are randomly selected and their BMIs are measured . It is given that the 99 % confidence interval for the population mean is ( 18.25 , 23.05 ) .
( a ) Find an unbiased estimate of the population mean .
Let
2
� be the known population variance .
[ 2 ]
( b ) Find � . [ 3 ]
2 . The number of goals in a league in the past few years is studied . 25 games are randomly selected and the numbers of goals are recorded . It is given that the 95 % confidence interval for the population mean is ( 2.995 , 3.365 ) .
( a ) Find an unbiased estimate of the population mean .
( b ) Find sn � 1. [ 3 ]
3 . The length of a rope , in centimetres , sold in a store is studied . 16 ropes are randomly selected and the corresponding lengths are measured . It is given that the sample mean is 37.5 cm and the width of the 95 % confidence interval for the population mean is 2.2 cm .
[ 2 ]
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( a ) Explain why the 90 % confidence interval for the population mean is a subset of the 95 % confidence interval for the population mean .
[ 1 ]
( b ) Write down the 95 % confidence interval for the population mean . [ 1 ]
( c ) Find sn � 1. [ 3 ]
4 . The width of a board , in centimetres , sold in a bazaar is studied . 9 boards are randomly selected and the corresponding widths are measured . It is given that the sample mean is 198 cm and the width of the 99 % confidence interval for the population mean is 12.8 cm .
( a ) Explain why the 95 % confidence interval for the population mean is a subset of the 99 % confidence interval for the population mean .
[ 1 ]
( b ) Write down the 99 % confidence interval for the population mean . [ 1 ]
Let
2
� be the known population variance .
( c ) Find � .
[ 3 ] www . seprodstore . com
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