Question

Suppose that a recent article stated that the mean time spent in jail by a first-time convicted burglar is 2.2 years. A study was then done to see if the mean time has increased in the new century. A random sample of 36 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. 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 and use α=0.01.

Answer 1

The null hypothesis states that there is no change in the mean length of jail time, while the alternative hypothesis states that there is an increase. We will use a one-sample t-test to test these hypotheses.

Step-by-step explanation:

To conduct a hypothesis test to determine if the mean length of jail time has increased, we need to set up null and alternative hypotheses. The null hypothesis, denoted as H0, states that there is no change in the mean length of jail time. The alternative hypothesis, denoted as H1, states that there is an increase in the mean length of jail time.

Null hypothesis: The mean length of jail time is equal to 2.2 years (μ = 2.2).

Alternative hypothesis: The mean length of jail time is greater than 2.2 years (μ > 2.2).

We will use a one-sample t-test with a significance level of α = 0.01 to test these hypotheses.