Question

The American Bar Association reports that the mean length of time for a hearing in juvenile court is 25 minutes. Assume that this this your population mean. As a lawyer who practices in the juvenile court, you think that the average hearing much shorter than this. You take a sample of 20 other lawyers who do juvenile work and ask them how long their last case in juvenile court was. The mean hearing length for this sample of 20 was 23 minutes., with a standard deviation of 6. Test the null hypotheses that the population mean is 25 minutes against the alternative that is less than 25. Set your alpha at .05.

Answer 1

Solution :

Given that,

Population mean = = 25

Sample mean = = 23

Sample standard deviation = s = 6

Sample size = n = 20

Level of significance = = 0.05

This is a left (One) tailed test,

The null and alternative hypothesis is,  

Ho: 25

Ha: 25

The test statistics,

t = ( - )/ (s/)

= ( 23 -25 ) / ( 6 /20)

= -1.491

Critical value of  the significance level is α = 0.05, and the critical value for a left-tailed test is

= -1.729

Since it is observed that t = -1.491 > = -1.729, it is then concluded that the null hypothesis is fails to reject.

P- Value = 0.0762   

The p-value is p = 0.0762 > 0.05, it is then concluded that the null hypothesis is fails to reject.

Conclusion :

It is concluded that the null hypothesis Ho is fails to reject. Therefore, there is not enough evidence to conclude that the mean length of time for a hearing in juvenile court is less than 25 minutes, at the 0.05 significance level.