Question

#12 In a random sample of 100 audited estate tax​ returns, it was determined that the mean amount of additional tax owed was ​$3416 with a standard deviation of ​$2547. Construct and interpret a​ 90% confidence interval for the mean additional amount of tax owed for estate tax returns. LOADING... Click the icon to view the​ t-distribution table. The lower bound is ​$ nothing. ​(Round to the nearest dollar as​ needed.) The upper bound is ​$ nothing. ​(Round to the nearest dollar as​ needed.) Interpret a​ 90% confidence interval for the mean additional amount of tax owed for estate tax returns. Choose the correct answer below. A. One can be​ 90% confident that the mean additional tax owed is less than the lower bound. 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 between the lower and upper bounds.

Answer 1

t critical value at 0.10 level with 99 df = 1.660

90% confidence interval for is

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

3416 - 1.660 * 2547 / sqrt(100) < < 3416 + 1.660 * 2547 / sqrt(100)

2993 < < 3839

Lower bound = $2993

Upper bound = $3839

One can be 90% confident that mean additional tax owed is between the lower and upper bounds.