Question

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: ___

Interpret and choose correct answer:

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

Answer 1

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 .