Exam 11: Comparing Two Populations or Treatments

Researchers have hypothesized that female Downy Woodpeckers food per tree. The data in the table at right are the bill lengths of 12 male and 12 female randomly selected Downy Woodpeckers caught and released in a banding survey.The investigators would like to know whether these data provide evidence that the males and females differ in bill size. a)Using a graphical display of your choosing, assess the plausibility of the assumption that the distributions of bill lengths are approximately normal.State your conclusion in a few sentences. b)Assuming that it is OK to proceed with a two-sample t procedure, determine if there is sufficient evidence to conclude that there is a difference in mean bill length for males and females. c)In a few sentences, state any concerns you have about your conclusions in part (b), based on your results from part (a).If you have no concerns, write "No concerns."

When comparing two population means, it is important to make the distinction between independent samples and paired samples.What makes two samples independent? avoid the feeding areas of socially dominant males; that is, the males chase them away from prime spots.An alternative opinion is that there are important physical characteristics of males and females that might lead them to choose different foraging locations.One such characteristic could be the bill length of the males and females; it may be that longer bills let one gender or the other drill deeper into a tree and thus get more

a)Using correct statistical notation, list these three alternative hypotheses. b)For each alternative hypothesis in part (a), give an example of a situation from your own experience or your reading where one might use that alternative hypothesis.Be sure to clearly specify a context, define your variables, and state the null and alternative hypothesis.

The P-value of an upper-tail t test is the area to the right of the calculated t value on the appropriate t curve.

The number of degrees of freedom of the two-sample t test are the same as the degrees of freedom for the paired t test statistic.

Two samples are said to be independent when the selection of the individuals in one sample has no bearing on the selection of those in the other sample.

As part of the foraging behavior assessment described in the previous problem, investigators also measured the bill depths of the male and female Downy Woodpeckers.Summary statistics for these measures are given in the table below: An initial analysis of the data revealed that it was reasonable to assume the bill depths for both sexes are approximately normal. a)Construct a 95% confidence interval for the difference in bill depths of the males and females. b)Do the data indicate that the bill depths differ? Justify your answer statistically.