A health scientist has collected data comparing the time in days from onset of flu-like respiratory symptoms as shown by a positive test result to a negative test result for vaccinated and unvaccinated persons. She wants to see if there is a significant difference in the time to a negative test. The data is summarized in the table below.

• What statistical test would be appropriate for this scenario and would it be right-tailed, left-tailed or two-tailed? Give the rationale for your choice.
• Calculate the standard error of the test statistic. Show the calculations.
• Calculate the value of the test statistic. Show the calculations.
• Look up the critical value of the test statistics using alpha .05 and state a decision based on the calculated value of the test statistic and provide a rationale for that decision.
• Calculate the effect size using Cohen's d and interpret that result

	Vaccinated	Unvaccinated
sample size n	31	31
mean days to negative test	6	9
sample SD (s)	2.0	3.0