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 = < Â
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.
