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 $2.5$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 three years with a standard deviation of $1.8$years. 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.

What symbol represents the random variable for this test?

Step by step solution

01

Introduction

Hypothesis testing may a kind of statistical reasoning that involves drawing conclusions a few population parameter or probability distribution using data from a sample. First, a supposition about the parameter or distribution is made.

02

Explanation

The variable quantity during this test is denoted by the Symbol $\mu$

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