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Chapter 9: Q. 41 (page 539)

Use the following information to answer the next seven exercises: Suppose that a recent article stated that the mean time spent in jail by a first-time convicted burglar is 2.5years. 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 three years with a standard deviation ofyears. Suppose that it is somehow known that the population standard deviation is 1.5. Conduct a hypothesis test to determine if the mean length of jail time has increased. Assume the distribution of the jail times is approximately normal.

Is this a test of means or proportions?

Short Answer

Expert verified

The given test is a mean test.

Step by step solution

01

Given information

The average sentence for a first-time burglar is 2.5 years in prison.

There were 26first-time burglars identified. The average length of time spent in prison is three years, with a standard variation of 1.8 years. The population standard deviation is 1.5.

02

Explanation

A hypothesis test is carried out to see if the average length of time spent in prison has increased. The distribution of jail time is customarily done. The average sentence for a first-time burglar is 2.5 years. This test determines whether the recent century's meantime is more than or equal to 2.5 years. This demonstrates that the exam was conducted on the basis of means.

To determine whether the mean is equal to or greater than 2.5 years, the hypothesis for this test is as follows:

H0:渭=2.5Ha:渭>2.5

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