Question

In a random sample of 64 audited estate tax returns, it was determined that the mean amount of additional tax owed was $3435 with standard deviation of $2559. 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 $. (Round to the nearest dollar as needed.) The upper bound is $(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 less than the lower bound, OC. One can be 90% confident that the mean additional tax owed is between the lower and upper bounds.

Answer 1

Note:  Since you have asked multiple questions, we will solve the first question for you. If you want any specific question to be solved then please specify the question number or post only that question.

Solution:

Given:

Sample mean = $\bar{x}$ = 3435

Standard deviation = s = 2559

Sample size = n = 64

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

Confidence level = 0.9, so level of significance = α=0.1

Critical tc = 1.669 ...Using excel formula, =TINV(0.1,63)

90% confidence interval for population mean is,

te x 8 te x 8 X X + In n

Calculation:

3435 1.669 x 2559 V64 1.669 x 2559 3435+ 64 (3435 – 534, 3435+534) (2901, 3969)

Lower bound = $2901

Upper bound = $3969

Hence, one can be 90% confident that the mean additional tax owned is between the lower and upper bounds.

Done