A study published in April 2000 in the British Medical Journal reported on a Scottish survey about high school students carrying weapons and engaging in illegal drug use.

a. Use software to carry out a z test to check for evidence that, in general, drug users are more likely than non-users to carry weapons. Report the sample proportions to be compared, the z statistic, and the P-value. State your conclusion in terms of relevant population proportions.

b. Use software to carry out a z test to check for evidence that, in general, those who carry weapons are more likely than those who don't carry weapons to use drugs. Report the sample proportions to be compared, the z statistic, and the Pvalue. State your conclusion in terms of relevant population proportions.

c. Use software to carry out a chi-square test to produce evidence of a relationship between using drugs and carrying weapons. Report the chi-square statistic and the P-value. State your conclusion in terms of a relationship between relevant variables.

d. In which case is the square of the z statistic approximately equal to the value of the chi-square statistic: when drug use is taken to be the explanatory variable, when carrying of weapons is taken to be the explanatory variable, or both of these, or neither of these?