24. Without external cues such as the sun, people attempting to walk in a

straight line tend to walk in circles (the accompanying image shows he paths

of two participants, PS and KS, attempting to walk in a straight line in an

unfamiliar forest on a cloudy day). One idea is that most individuals have a

tendency to turn in one direction because internal physiological asymmetries,

or because of differences between legs in length or strength. Souman et al.

tested for a directional tendency by blindfolding 15 participants in a large

field and asking them to walk in a straight line. The numbers below are the

median change in direction (turning angle) of each of the 15 participants

measured in degrees per second. A negative angle refers to a left turn, whereas

a positive number indicates a right turn.

-5.19, -1.20, -0.50, -0.33, -0.15, -0.15, -0.15, -0.07, 0.02, 0.02, 0.28, 0.37, 0.45, 1.76,

2.80.

a. Draw a graph showing the frequency distribution of the data. Is a trend in

the mean angle suggested?

b. Do people tend to turn in one direction (e.g. left) more on average than the

other direction (e.g right)? Test whether the mean angle differs from zero.

c. Based on your results in part (b), is the following statement justified?

People do not have a tendency to turn more in one direction, on average,

than the other direction. Explain.

Two different researchers measured the weight of two separate samples of ruby-throated hummingbirds from the same population. Each calculated a 95% confidence interval for the mean weight of these birds.Researcher 1 found the 95% confidence interval to be 3.12g < <3.48g,while Researcher 2 found the 95 % confidence interval to be 3.05g < < 3.62g.

a)How could the two researchers get different answers? b)Which researcher most likely had the larger sample? c)Can you be certain about your answer in part (b)?Why or Why not?

18.!In!Europe!53%!of!flowers!of!the!rewardless!orchid,!Dactylorhiza,sambucina,!are!yellow,! whereas!the!remaining!flowers!are!purple!(Gigord!et!al.!2001).!For!the!following,!you!may!use! the!normal!approximation!only!if!it!is!appropriate!to!do!so.!

a.If we!took!a!random!sample!of!a!single!individual!from!this!population,!what!is!the!probability!

that!it!would!be!purple?!

b.!If!we!took!a!random!sample!of!5!individuals,!what!is!the!probability!that!at!least!3!are!

yellow?!

c.!If!we!took!many!samples!of!n!=!5!individuals,!what!is!the!expected!standard!deviation!of!the!

sampling!distribution!for!the!proportion!of!yellow!flowers?!

d.!If!we!took!a!random!sample!of!263!individuals,!what!is!the!probability!that!no!more!than!150!

are!yellow?!