Question

In a random sample of

38

criminals convicted of a certain​ crime, it was determined that the mean length of sentencing was

55

​months, with a standard deviation of

8

months. Construct and interpret a

95​%

confidence interval for the mean length of sentencing for this crime.Click here to view the standard normal distribution table (page 1).

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Click here to view the standard normal distribution table (page 2).

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Click here to view the table of critical t-values.

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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.There is a

95​%

probability that the mean length of sentencing for the crime is between

nothing

and

nothing

months.

B.

95​%

of the sentences for the crime are between

nothing

and

nothing

months.

C.We can be

95%

confident that the mean length of sentencing for the crime is between

nothing

and

nothing

months.

Answer 1

t critical value at 0.05 significance level with 37 df = 2.026

95% confidence interval for is

- t * S / sqrt(n) < < + t * S / sqrt(n)

55 - 2.026 * 8 / sqrt(38) < < 55 + 2.026 * 8 / sqrt(38)

52.4 < < 57.6

95% CI is (52.4 , 57.6)

We can be 95% confident that the mean length of sentencing for a crime is between 52.4 and 57.6 months.