Question

STATISTIC REVIEW

Anystate Auto Insurance Company took a random sample of 370 insurance claims paid out during a 1-year period. The average claim paid was $1570. Assume the standard deviation is $250.

Find 0.90 and 0.99 confidence intervals for the mean claim payment.

Answer 1

Z for 0.90 CI = 1.645

so,

0.90 CI = ( mean-z*sd/sqrt(n) , mean+z*sd/sqrt(n) )

= ( 1570-1.645*250/sqrt(370) , 1570+1.645*250/sqrt(370) )

= ( 1548.62 , 1591.38 )

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Z for 0.99 CI = 2.575

so,

0.99 CI = ( mean-z*sd/sqrt(n) , mean+z*sd/sqrt(n) )

= ( 1570-2.575*250/sqrt(370) , 1570+2.575*250/sqrt(370) )

= ( 1536.53 , 1603.47 )

Answer 2

Z for 0.90 CI = 1.645

0.90 CI = ( 1570 - 1.645*250/sqrt(370) 1570 + 1.645*250/sqrt(370) )

= ( $1548.62 , $1591.38 )

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Z for 0.99 CI = 2.575

0.99 CI = ( 1570 - 2.575*250/sqrt(370) 1570 + 2.575*250/sqrt(370) )

= ( $1536.53 , $1603.47 )