Assignment #6: Hypothesis Testing for One Population Mean & Proportion 1. We an: interested in the average dollar amount lost by victims of burglary. The National Insurance Association has reported that the mean dollar amount lost by victims ot'burglary is $2,222. Assume that this is the population mean. We believe that the true population mean loss is different from this. Formallyr state the null and research hypotheses we would test to investigate this question. What if we believed the dollar amount to be higher? 2. While previous research has consistently found a relationship between dropping out of high school and crime. Christopher Dennison {2020} expanded upon this and found a relationship bettnreen dropping out of college and offending. Hypothetically. those who dropped out of college reported offending 5 times per year. We believe the true population mean to be less than this, After collecting our own sample of 29 college dropouts. we find that the mean number of times they have offended during a 1year period was ll=2 with a standard deviation equal to 1.5. Pertorm all of the procedures necessary for conducting a hypothesis test based on our assumption. What do you conclude? Set your alpha level at .05. 3. A study conducted byesearch Institute otAmerica has concluded that the average number of hours inmates at state correctional facilities spend in their cells during a day is 15. We believe the population mean number of hours to be different from this. We contacted a sample of 15 state correctional facilities and inquired about the mean number of hours that inmates housed in these facilities spent in their cells. We came up with the foltowing sample data: Facility Number Hours Spent in Cells Calculate the mean number of hours inmates spend in their cells from the sample data. Test the null hypothesis that the mean number of hours inmates spend in their cells is 15 against the null hypothesis that it is different from that. Set your alpha level at .05. Hint: You will also have to calculate the standard deviation. Remember. practice makes pen'ectl What do you conclude? 4. 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 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 5. Test the null hypothesis that the population mean is 25 minutes against the alternative that it is less than 25. Set your alpha level at .05