Why some rules are more likely to be broken

The Harvard Business Review headline suggests that employees break rules within the workplace. In a sample of 100 employees, the average employee violated rules 33 rules per year. Suppose the population standard deviation is 13 violated rules. Answer the following questions:

(a) Is there enough evidence to suggest that the average number of rule violations exceeds 30? Using the test statistic method, show all steps for your hypothesis test. Also, use a 5% significance level.

(b) Re-do part (a) using the p-value method.

(c) Re-do part (b) using the p-value method and a 1% significance level.

(d) In words, explain why someone might use a 1% significance level for making conclusions instead of a 5% significance level.