Male and Female Downy Woodpeckers (Picoides Pubescens)

Essay

Male and female Downy Woodpeckers (Picoides pubescens)
The data in the table at right are the bill lengths of 12 male and12 female randomly selected Downy Woodpeckers caught andreleased in a banding survey. The investigators would like toknow whether these data provide evidence that the male andfemale Downy Woodpeckers differ in mean bill length. Aninitial analysis of the data established the plausibility that thedistributions of bill lengths are approximately normal.
a) Construct a 95% confidence interval for the difference in mean bill length formales and for females.
b) Do the data indicate that the mean bill length differs for males and females?
Provide an appropriate statistical justification using your response in part (a).