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 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. 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

Solution:

Given:

the mean time spent in jail by a first-time convicted burglar is 2.2 years.

Thus Mean =

Sample size = n = 26

Sample mean =

Sample standard deviation =s = 1.8

We have to test  if the mean length of jail time has increased

Level of significance = 0.01

Step 1) State H0 and H1:

Vs

Step 2) Test statistic:

Step 3) t critical value

df = n - 1 = 26 -1 = 25

Level of significance = 0.01

Since this right tailed( one tailed) test , look for one tail area = 0.01 and df = 25

t critical value = 2.485

Step 4) Decision Rule:

Reject null hypothesis H0, if absolute t test statistic value > t critical value = 2.485 , otherwise we fail to reject H0

Since t test statistic value = 2.266< t critical value = 2.485 , we fail to reject H0.

Step 5) Conclusion:

At 0.01 level of significance, there is not sufficient evidence to conclude that: the mean length of jail time has increased.