Discuss the below:
Q1. Ten years ago, the mean age of all juveniles held in public custody was 16.0 years, as reported by the U.S. Office of Juvenile Justice and Delinquency Prevention in Children in Custody. The ages of a random sample of juveniles currently being held in public custody are to be used to decide whether this year's mean age of all juveniles being held in public custody is less than it was 10 years ago.
a. Determine the null hypothesis.
b. Determine the alternative hypothesis.
c. Classify the hypothesis test as two-tailed, left-tailed, or right-tailed.
Q2. The Census Bureau publication Census of Population and Housing reports that the mean travel time to work in 1990 for all North Dakota residents was 13 minutes. A transportation official obtained this year's travel times, in minutes, for a random sample of 35 North Dakota residents. Here are the data.
29 40 0 12 10 6 41 25 21 5 4 19 2 7
10 8 3 6 52 4 12 0 33 6 2 17 21 8
38 2 13 8 14 11 2
At the 5% significance level, do the data provide sufficient evidence to conclude that the mean travel time to work for all North Dakota residents has changed from the 1990 mean of 13 minutes? Assume σ = 11.6 minutes.