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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.

Is $蟽$known and, if so, what is it?

Step by step solution

01

Introduction

Hypothesis testing may be a variety of inferential statistics that permits us to create inferences a few whole population from little sample. Working with a sample incorporates a lot of benefits.

02

Explanation

The root of the variance of a collection of integers is employed to calculate the population variance. It's wont to calculate a confidence interval before making a choice (such as accepting or rejecting a hypothesis). Sample variance could be a slightly more complicated computation.

$蟽=1.5$ is that the population variance.

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