Question

In a random sample of 49 audited estate tax​ returns, it was determined that the mean amount of additional tax owed was $3412 with a standard deviation of 2564.

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

Answer 1

t critical value at 0.10 significance level with 48 df = 1.677

90% confidence interval for is

- t * S / sqrt(n) < < + t * S / sqrt(n)

3412 - 1.677 * 2564 / sqrt(49) < < 3412 + 1.677 * 2564 / sqrt(49)

2798 < < 4026

90% CI is ( $2798 , $4026 )

Interpretation = WE are 90% confident that mean additional amount of tax owed for estate tax return is

between $2798 and $4026