Suppose that a recent article stated that the mean time spent injail by a first-time convicted burglar is 2.5 years. A study wasthen done to see if the mean time has increased in the newcentury.

A random sample of 26 first-time convicted burglars in a recentyear was picked. The mean length of time in jail from the surveywas 3 years. Suppose that it is somehow known that the populationstandard deviation is 1.5 years.

Conduct a hypothesis test to determine if the mean length of jailtime has increased. Assume the distribution of the jail times isapproximately normal. Use a 1% level of significance.

a.) What is α? State the null and alternatehypotheses. Will you use a left-tailed, right-tailed, or two-tailedtest?

αα =

H0H0: μμ =

H1H1: μμ Select an answer > not = <  

The test is a Select an answer left-tailed right-tailedtwo-tailed  test

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

The best sampling distribution to use is the Select an answerStudent's t Normal  distribution.

The test statistic (z or t value) is =

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

The p-value is =

d.) Conclude the test.

Based on this we will Select an answer Reject Fail toreject  the null hypothesis.