Question

# In a random sample of 64 audited income tax returns, it was determined that the mean...

In a random sample of 64 audited income tax returns, it was determined that the mean amount of additional tax owed was \$3448 with a standard deviation of \$2580. Construct and interpret a 90% confidence interval for the mean additional amount of tax owed for income tax-returns.

Lower bound: ___

Upper bound: ___

A) One can be 90% confident that the mean additional tax owed is between the lower and upper bounds

B) One can be 90% confident that the mean additional tax owed is greater than the upper bound

C) One can be 90% confident that the mean additional tax owed is less than the lower bound

Solution :

Given that,

Z/2 = 1.645

Margin of error = E = Z/2* ( /n)

= 1.645 * (2580 / 64)

= 531

At 90% confidence interval estimate of the population mean is,

- E < < + E

3448 - 531 < < 3448 + 531

2917< < 3979

Lower bound = \$ 2917

Upper bound = \$ 3979

A) One can be 90% confident that the mean additional tax owed is between the 2917 and 3979 .

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