Using the z-distribution, it is found that since the <u>test statistic is greater than the critical value</u>, it can be concluded that the mean length of jail time has increased.
At the null hypothesis, it is <u>tested if the mean length of jail time is still of 2.5 years</u>, that is:
At the alternative hypothesis, it is <u>tested if it has increased</u>, that is:
We have the <u>standard deviation for the population</u>, thus, the z-distribution is used. The test statistic is given by:
The parameters are:
is the sample mean.
is the value tested at the null hypothesis.
is the standard deviation of the sample.
- n is the sample size.
For this problem, the values of the <u>parameters</u> are:
Hence, the value of the <u>test statistic</u> is:
The critical value for a <u>right-tailed test</u>, as we are testing if the mean is greater than a value, with a <u>significance level of 0.05</u>, is of
Since the <u>test statistic is greater than the critical value</u>, it can be concluded that the mean length of jail time has increased.
A similar problem is given at brainly.com/question/24166849