In a study in Alameda County, California, researchers compared the demographic characteristics of members of grand juries to determine how closely these juries reflected the population of the county. If the juries were selected randomly or impartially, then the characteristics of the jurors should closely match those of the larger county; however, if attorneys were tilting the jury selection process, then the jurors' characteristics would be quite different from the county. (figures taken from UCLA Law Review, vol 20, 1973 - as shown at: https://www.stat.ucla.edu/cases/jury/)
Age Country-Wide % # of Jurors
21-40 42 5
41-50 23 9
51-60 16 19
>61 19 33
Total 100 62
Questions:
· Based on the figures shown in the table above, use the chi-square test to evaluate whether there is evidence of jury fixing in terms of the age of jurors in Alameda County.
· What is the null hypothesis? What is the alternative hypothesis?
· What figures do you need to calculate for this test?
· How many degrees of freedom are there?
· What is the value of the chi-square statistic for this table? What is the p-value of this statistic?
· From this value, what can you conclude about the age of jurors in Alameda County?