Question

The American Bar Association reports that the mean length of time for a hearing in juvenile court is 25 minutes. Assume that this is your population mean. As a lawyer who practices in the juvenile court, you think that the average hearing is much shorter than this. You take a random 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 hearings was 23 minutes, with a standard deviation of 6. Test the null hypothesis that the population mean is 25 minutes against the alternative that it is less than 25. Using this information and an alpha level of .05, perform all the procedures necessary for conducting a hypothesis test.

1. Conduct the appropriate t test, then enter the value of the t_obt score you computed in the box. Round to two decimal places.

2. Which of the following is the appropriate critical t value for this test?

A. -2.093

B. -2.086

C. -1.729

D. 1.725

E. 1.645

3.Which of the following statements is the most appropriate conclusion to draw from this test?

A. Since tobt is less than tcrit, we reject the null hypothesis.

B. Since tobt is not less than tcrit, we fail to reject the null hypothesis.

C. Since tobt is less than tcrit, we fail to reject the null hypothesis.

D. Since tobt is not less than tcrit, we fail to reject the alternative hypothesis.

E. Since tobt is greater than tcrit, we have proven the alternative hypothesis.

Answer 1

Given
X bar	23
μ0	25
S	6
n	20

Hypothesis :		α=	0.05
		df	19	n-1
Ho:	μ = μ0
Ha:	μ​ < μ0
t Critical Value :
tc	-1.729132812	T.INV(alpha,df)	LEFT
ts	<=	tc	LEFT	To reject
Test :
ts	-1.490711985	(X bar-μ)/(S/SQRT(n))
P value :
p	0.076226291	T.DIST(ts,df,TRUE)	LEFT
Decision :
P value	>	α	Do not reject

ANS:

1)  t_obt score = -1.4907

2) t critical = -1.729

3) B. Since tobt is not less than tcrit, we fail to reject the null hypothesis.