In a random sample of 100 audited estate tax returns, it was determined that the mean amount of additional tax owed was $3418 with a standard deviation of $2560. Construct and interpret a 90% confidence interval for the mean additional amount of tax owed for estate tax returns. What are the lower and upper bounds?
Solution :
Given that,
Point estimate = sample mean =
= $3418
Population standard deviation =
= $2560
Sample size = n =100
At 90% confidence level
= 1 - 90%
= 1 - 0.90 =0.10
/2
= 0.05
Z/2
= Z0.05 = 1.645( Using z table ( see the 0.05 value in
standard normal (z) table corresponding z value is 1.645 )
Margin of error = E = Z/2
* (
/n)
= 1.645* ( 2560 / 100
)
=421.12
At 90% confidence interval estimate of the population mean
is,
- E <
<
+ E
3418 - 421.12 <
< 3418 + 421.12
2996.88 <
< 3839.12
lower bound 2996.88 and upper bound =3839.12
( 2996.88 ,3839.12 )At 90% confidence interval estimate of the
population mean is between lower bound =2996.88 and upper bound
=3839.12)
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