Question

In a random sample of

81

audited estate tax​ returns, it was determined that the mean amount of additional tax owed was

​$3409

with a standard deviation of

​$2533.

Construct and interpret a​ 90% confidence interval for the mean additional amount of tax owed for estate tax returns.

Answer 1

Solution :

Given that,

= 3409

s = 2533

n = 81

Degrees of freedom = df = n - 1 = 81 - 1 = 80

At 90% confidence level the t is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

t _/2,df = t_0.05,80 = 1.664

Margin of error = E = t_/2,df * (s /n)

= 1.664 * (2533 / 81)

= 468.3

Margin of error = 468.3

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

- E < < + E

3409 - 468.3 < < 3409 + 468.3

2940.7 < < 3877.3

(2940.7, 3877.3 )