In: Statistics and Probability
n a random sample of 38 criminals convicted of a certain crime, it was determined that the mean length of sentencing was 70 months, with a standard deviation of 5 months. Construct and interpret a 95% confidence interval for the mean length of sentencing for this crime.
We have given that,
Sample mean =70 months
Sample standard deviation =5 months
Sample size =38
Level of significance=1-0.95=0.05
Degree of freedom =37
t critical value is (by using t table)=2.026
Confidence interval formula is
=(68.36,71.64)
We are 95% confident that population mean length of
sentencing for this crime is between 68.36 months to 71.64
months.