Suppose that a recent article stated that the mean time spent in jail by a first

Question

Suppose that a recent article stated that the mean time spent in jail by a first-time convicted burglar is 2.5 years. A study was then done to see if the mean time has increased in the new century. A random sample of 26 first-time convicted burglars in a recent year was picked. The mean length of time in jail from the survey was 3 years with a standard deviation of 1.8 years.Suppose that it is somehow known that the population standard deviation is 1.5. If you were conducting a hypothesis test to determine if the mean length of jail time has increased, what would the null and alternative hypotheses be? The distribution of the population is normal.

(a) null hypothesis

H0: = 2.5 yearsH0: = 3 years    

H0: > 3 yearsH0: 2.5 yearsH0: = 1.8 years

(b) alternative hypothesis

Ha: 2.5 yearsHa: > 3 years   

Ha: 1.8 yearsHa: 3 yearsHa: > 2.5 years

Explanation / Answer

Here we need to test the claim whether the mean length of jail time has increased or not. Hence,

Our null and alternative hypotheses will be:

a) Null Hypothesis:

H0: = 2.5 years

b) Alternative Hypothesis:

Ha: > 2.5 years

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