3. Confidence Intervals, Hypothesis Tests, and Chi Square a. A random sample of 41 Brisbane adults report that they perceive that the average cost of property crime for an individual is $160, with a standard deviation of $52. i. Identify and describe the correct probability distribution and explain why this is appropriate (1 mark) ii. Construct a 99% confidence interval to estimate the population mean for "average cost of property crime for the individual" for all Brisbane adults as a whole. Fully interpret the interval (2 marks) iii. Assume that we know that in the Queensland population, the mean perceived average cost of property crime for an individual is $85. Is the Brisbane sample significantly different from the Queensland average? Stata has provided you with an obtained t value of 7.29. Use an alpha of 0.01 (2 marks) b. Social science researchers are trying to understand what types of attitudes are related to views about crime and punishment. A random sample of Australians was surveyed about crime and punishment, and political preferences. Below is a contingency table showing the distribution of respondents' preferred party (ALP or LIB/NAT) and whether they support the introduction of harsher sentences for criminal offenders (YES or NO). Do you Lib/Nat ALP Totals support the introduction of harsher sentences for criminal offenders? Yes 526 359 885 No 403 631 1034 Totals 929 990 1919 Is there a statistically significant relationship between these variables? You can use the table below for your working. (3 marks) Step 1 Step 2 Step 3 Step 4 Step5 to to-fe fo-fe) 2 to-fe) Life ii. Compute the column percentages to determine the pattern of the relationship. Which group is more likely to think that harsher sentences for criminal offenders should be implemented