Suppose that a recent article stated that the mean time spent in jail by a first-time convicted burglar is 3.7 years. A study was then done to see if the mean time has decreased in the new century.

A random sample of 46 first-time convicted burglars in a recent year was picked. The mean length of time in jail from the survey was 3 years. Suppose that it is somehow known that the population standard deviation is 1.8 years.

Conduct a hypothesis test to determine if the mean length of jail time has decreased. Assume the distribution of the jail times is approximately normal. Use a 1% level of significance.

a.)What is ? State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test?

=

H0H0: =

H1H1: Select an answer not = < >

The test is a Select an answer right-tailed left-tailed two-tailedtest

b.)Identify the Sampling Distribution you will use. What is the value of the test statistic?

The best sampling distribution to use is the Select an answer Student's t Normaldistribution.

The test statistic (z or t value) is =

c.)Find or estimate the P-value for the test.

The p-value is =

d.)Conclude the test.

Based on this we will Select an answer Reject Fail to rejectthe null hypothesis.