1. A statistics instructor, white guy with spikey hair and glasses, is curious to know how much cash students carry these days. On a random day, he asks the 48 students who are in attendance to check how much money they have on them. The results are X= $22.25, S= $6.62

A: Is this sample sufficient to meet the normality criteria?

B:Use this sample to construct a 95% confidence interval for the average amount of cash carried by all students at the college.

C: Interpret the meaning of this interval in the context of cash money.

2. A study from 2016 titled "Comparing Black and White Drug Offenders: Implications for Racial Disparities in Criminal Justice and Reentry Policy and Programming" found that the average sentence for drug-related offences was 16.0 months. This average includes both white and black offenders. Disaggregating the data, looking only at the sample of 86 black offenders, the average sentencing was 20.9 months, with a sample standard deviation of 9.1 months*.

A: Does this show that black offenders receive prison sentences significantly longer than 16 months? Conduct a hypothesis test at the 1% significance level. Make sure to:

Include an appropriate hypotheses

Calculate standard error

Calculate the test statistic

Calculate tail probability and find P-Value

Find an appropriate conclusion

B: What does this conclusion mean in the context of the problem?