Question

In a random sample of

100

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

​$3478

with a standard deviation of

​$2555

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

The lower bound is $:

The upper bound is $:

Answer 1

Solution :

Given that,

Point estimate = sample mean = = $3478

sample standard deviation = s = $2555

sample size = n = 100

Degrees of freedom = df = n - 1 =100-1=99

At 90% confidence level the t is ,

= 1 - 90% = 1 - 0.90 = 0.1

/ 2 = 0.1/ 2 = 0.05

t /2,df = t0.05,99 = 1.660

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

= 1.660* (2555 / 100)

Margin of error = E = 424.1

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

- E < < + E

3478 - 424.1 < < 3478 + 424.1

3053.9 < < 3902.1

($3053.9,$3902.1) , First we find df by the formula (n- 1),then find t-value,then margin of error.then find 90 % confidence interval i.e ($3053.9,$3902.1).