Final answer:
Mary Jo Fitzpatrick can use hypothesis testing and the P-value to determine if there is a statistically significant difference in wages between unionized and non-unionized nurses. If the p-value is less than the .02 significance level, she can conclude that union nurses earn more, subject to the validity of her statistical model and data.
Step-by-step explanation:
Mary Jo Fitzpatrick, the vice president for Nursing Services at St. Luke's Memorial Hospital, has observed that unionized nurses tend to have higher wages in job postings. To determine if union nurses indeed earn more, one needs to statistically analyze wage data for both unionized and non-unionized nurses using hypothesis testing at a given significance level, in this case, .02. The P-value is a crucial component in this process; it indicates the probability of obtaining results at least as extreme as the ones observed during the test, assuming that the null hypothesis is true. Mary has noted that the process of rejecting the null hypothesis occurs when the p-value is less than the chosen significance level.
In a similar statistical analysis mentioned, a conclusion was drawn that at a 5 percent significance level, there was sufficient evidence to conclude that the mean salary of California registered nurses exceeds a certain amount. Thus, if Mary discovers a p-value less than .02 in her investigation, she could conclude that there is a statistically significant difference in wages between unionized and non-unionized nurses at the 2 percent significance level. However, it is important to note that other factors can also influence nurses' salaries, such as location, experience, and employer.