Question

In a random sample of 64 audited estate tax​ returns, it was determined that the mean amount of additional tax owed was ​$3445 with a standard deviation of ​$2593. Construct and interpret a​ 90% confidence interval for the mean additional amount of tax owed for estate tax returns. LOADING... Click the icon to view the​ t-distribution table. The lower bound is ​$ 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 greater than the upper bound. B. One can be​ 90% confident that the mean additional tax owed is between the lower and upper bounds. C. One can be​ 90% confident that the mean additional tax owed is less than the lower bound

Answer 1

Solution :

degrees of freedom = n - 1 = 64 - 1 = 63

t/2,df = t_0.05,63 = 1.669

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

= 1.669 * (2593 / 64)

Margin of error = E = 541

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

  ± E  

= 3445  ± 541

= ( $ 2904, $ 3986 )

lower bound = $ 2904

upper bound = $ 3986

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