In a random sample of 81 audited estate tax returns, it was determined that the mean amount of additional tax owed was $3408 with a standard deviation of $2565. construct and interpret a 90% confidence interval for the mean additional amount of tax owed for estate tax returns. the lower bound is $ nothing. (round to the nearest cent as needed.) the upper bound is $ nothing. (round to the nearest cent 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 between the lower and upper bounds
c. one can be 90% confident that the mean additional tax owed is greater than the upper bound.

Using the t-distribution, it is found that:

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

We are given the standard deviation for the sample, which is why the t-distribution is used to solve this question.

The information given is:

Sample mean of .

Sample standard deviation of .

Sample size of .

The confidence interval is:

The critical value, using a t-distribution calculator, for a two-tailed 90% confidence interval, with 81 - 1 = 80 df, is t = 1.6641.

Then, the bounds of the interval are:

The lower bound is $2,933.73.

The upper bound is $3,822.27.

The interpretation is that we are 90% sure that the true mean is in the interval, that is, option b.

A similar problem is given at link

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

Step-by-step explanation:

Given:

n= 81

Solution:

A confidence interval, in statistics, refers to the probability that a population parameter will fall between two set values for a certain proportion of times. Confidence intervals measure the degree of uncertainty or certainty in a sampling method. A confidence interval can take any number of probabilities, with the most common being a 95% or 99% confidence level.

Confidence interval =

To Find the z  value:

Degree of freedom = n-1

=>81- 1

=> 80

Significance level = 1- confidence level

=>

=>

=>

=>0.05

using this value In T- Distribution table we get

z =  1.645

Substituting the values  we have,

confidence interval =

confidence interval =

confidence interval =

confidence interval =

confidence interval= (2939.18, 3876.83)

w'x is 0.

hope it

2. angles qrt and qst both measures 156 degrees.

step-by-step explanation:  

we have been given a diagram of a circle and we are told that measure of arc qvt is 156 degrees.  

we can see from our given diagram that angle qrt and angle qst subtends to arc qvt.

since we know that angles subtended by the same arc at the circumference are always equal.

by angle subtended by same arc theorem, measure of angle qrt and angle qst will be equal to the measure of arc qvt.

therefore, angles qrt and qst both measures 156 degrees and 2nd statement is the correct choice.