(Question 1) In a random sample of 33criminals convicted of a certain crime, it
ID: 2930830 • Letter: #
Question
(Question 1)
In a random sample of 33criminals convicted of a certain crime, it was determined that the mean length of sentencing was 62 months, with a standard deviation of 8 months. Construct and interpret a 95% confidence interval for the mean length of sentencing for this crime.
Select the correct choice below and fill in the answer boxes to complete your choice.
(Use ascending order. Round to one decimal place as needed.)
A. We can be 95% confident that the mean length of sentencing for the crime is between ____ and _____ months.
B. There is a 95% probability that the mean length of sentencing for the crime is between ___ and ____ months.
C. 95% of the sentences for the crime are between _____ and ____months.
(Question 2)
In a random sample of 64 audited estate tax returns, it was determined that the mean amount of additional tax owed was $3433 with a standard deviation of $2539.
Construct and interpret a 90% confidence interval for the mean additional amount of tax owed for estate tax returns.
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.
C. One can be 90% confident that the mean additional tax owed is between the lower and upper bounds.
Explanation / Answer
Ans:
As, n>=30,so central limit theorm is applicable(we can assume distribution of sample means is normally dstributed)
z value for 95% Confidence interval is 1.96
95% Confidence interval
=62+/-1.96*(8/sqrt(33))
=62+/-2.73
=(59.27,64.73)
We can be 95% confident that the mean length of sentencing for the crime is between 59.27and 64.73 months.
2)z value for 90% CI is 1.645
90% CI
=3433+/-1.645*(2539/sqrt(64))
=3433+/-522.08
=(2910.92,3955.08)
The lower bound is 2910.92
The upper bound is 3955.08
One can be 90% confident that the mean additional tax owed is between the lower and upper bounds.
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