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In: Statistics and Probability

In a random sample of 100 audited estate tax​ returns, it was determined that the mean...

In a random sample of 100 audited estate tax​ returns, it was determined that the mean amount of additional tax owed was ​$3494 with a standard deviation of ​$2527. Construct and interpret a​ 90% confidence interval for the mean additional amount of tax owed for estate tax returns.

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Expert Solution

( , )

Solution :

Given that,

Point estimate = sample mean = = 3494


Population standard deviation =    = 2527
Sample size = n =100

At 90% confidence level the z is

= 1 - 90% = 1 - 0.90 = 0.1

/ 2 = 0.1 / 2 = 0.05

Z/2 = Z0.05 = 1.645 ( Using z table )


Margin of error = E = Z/2    * ( /n)

= 1.645 * (2527 /  100 )

= 415.7
At 90% confidence interval
is,

- E < < + E

3494 - 415.7 <   < 3494+ 415.7

3078.3 <   < 3909.7

orchestra answered 2 years ago
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