In a random sample of 31 criminals convicted of a certain crime, it was determin

Question

In a random sample of 31 criminals convicted of a certain crime, it was determined that the mean length of sentencing was 62 months, with a standard deviation of 12 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.

__________________________________________________________________________________________________

In a random sample of 81 audited estate tax returns, it was determined that the mean amount of additional tax owed was $3418 with a standard deviation of $2583. 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 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.

Explanation / Answer

1) here std error of mean =std deviation/(n)1/2 =12/(31)1/2 =2.155

for 95%  confidence interval ; z=1.96

hence confidence interval =sample mean -/+ z*std error =62 -/+ 1.96*2.155 =57.8 ; 66.2

hence option A is correct:

We can be 95% confident that the mean length of sentencing for the crime is between 57.8 and 66.2.

2)

std error of mean =std deviation/(n)1/2 =2583/(81)1/2 =287

for 90%  confidence interval ; z=1.645

hence confidence interval =sample mean -/+ z*std error =2945.927 ; 3890.073

The lower bound is 2946

The upper bound is 3890

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

please revert I have used here z distribution for sample size greater then 30 ; some books refer t distribution for unknown population std deviation

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