A computer security consultant is interested in determining the most secure password conditions. One rule requires users to include at least one special character (*, @, !, %, or $); others don't. Consultants created 100,000 accounts for this experiment and watched the accounts for six months, carefully monitoring them for inappropriate logins. Among the 50,000 accounts with passwords that used special characters, there were 1,055 security breaches or threats. Meanwhile, among the 50,000 who did not use special characters, 2,572 security violations occurred.

a. Explain what statistical test is most appropriate to solve this problem and include the reasons!

b. Assume that researchers claim password systems have significant differences in their security strength. What null and alternative hypotheses are appropriate for this study?

c. Using a significance level of 0.05 and the alternative hypothesis (mentioned in point b), what decision do you arrive at from this statistical test?