A Head-up Display (HUD) is a transparent display that permits the user to maintain their viewpoint while also being able to view additional information that may be relevant to their task. You have been asked to design a study to evaluate a new aircraft HUD to determine if the display affects the pilot's reaction time for a particular task. Specifically, the concern is if the reaction time will be more than 20 ms from the nominal reaction time. Previous data supports that the standard deviation on the reaction time for the particular task was 30 ms. Required:
a. Based on the information provided, what is the Cohen’s d effect size of interest that you should consider for designing your study?
b. How many subjects will you need for your study if you want to detect the effect size from part (a) with a power of 90% and a level of significance of 1% for examining if there is a larger reaction time?
c. How many subjects would you need for your study if you want to estimate the confidence interval on the mean reaction time with 99% confidence and a confidence interval width of ±10 ms?