Question

9.3

In a random sample of 81 audited estate tax returns, it was determined that the mean amount of additional tax owed was $3425 with a standard deviation of $2547. Construct and interpret a 90% confidence interval for the mean additional amount of tax owed for estate tax returns. Click the icon to view the t-distribution table. The lower bound is 2960 (Round to the nearest dollar as needed.)

Answer 1

Solution:

Given:

Sample mean = = 3425

r

Sample standard deviations=s=2547

Sample size = n = 81

Degrees of freedom = df = n-1=80

Confidence level = 0.90

So, level of significance = α=0.1

The critical t-value = tc = 1.664 ...Using excel formula, =TINV(0.1,80)

The 90% confidence for the population mean μ:

te x 8 te x 8 in X + n

Calculation:

3425 1.664 x 2547 .3425 + V81 1.664 x 2547 V81 (3425 - 470.947, 3425 + 470.947) (2954.053, 3895.947)

Rounding to nearest dollar.

Lower bound = $ 2954

Done