1) In a random sample of 49 audited estate tax returns, it was determined that t
ID: 3220372 • Letter: 1
Question
1) In a random sample of 49 audited estate tax returns, it was determined that the mean amount of additional tax owed was $3453 with a standard deviation of $2537. Construct and interpret a 90% confidence interval for the mean additional amount of tax owed for estate tax returns.
The lower bound is: (round to the nearest dollar as needed)
The upper bound is: (round to the nearest dollar as needed).
2) In a random sample of 64 audited estate tax returns, it was determined that the mean amount of additional tax owed was $3413 with a standard deviation of $2516. Construct and interpret a 90% confidence interval for the mean additional amount of tax owed for estate tax returns.
The lower bound is: (round to the nearest dollar as needed)
The upper bound is: (round to the nearest dollar as needed)
Explanation / Answer
(1)
n = 49
x-bar = 3453
s = 2537
% = 90
Standard Error, SE = s/n = 2537/49 = 362.4285714
Degrees of freedom = n - 1 = 49 -1 = 48
t- score = 1.677224197
Width of the confidence interval = t * SE = 1.67722419660282 * 362.428571428571 = 607.8739695
Lower Limit of the confidence interval = x-bar - width = 3453 - 607.873969540194 = 2845.12603
Upper Limit of the confidence interval = x-bar + width = 3453 + 607.873969540194 = 4060.87397
The 90% confidence interval is [$2845, $4061]
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