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Chapter 6, Section 2-HT, Exercise 122

Be Nice to Pigeons, As They Remember Your Face

In a study1 conducted in Paris, France, equal amounts of pigeon feed were spread on the ground in two adjacent locations. A person was present in both sites, with one acting hostile and running at the birds to scare them away and the other acting neutral and just observing. The two people were randomly exchanged between the two sites throughout and the birds quickly learned to avoid the hostile person’s site and to eat at the site of the neutral person. At the end of the training session, both people behaved neutrally but the birds continued to remember which one was hostile. In the most interesting part of the experiment, when the two people exchanged coats (orange worn by the hostile one and yellow by the neutral one throughout training), the pigeons were not fooled and continued to recognize and avoid the hostile person. The quantity measured is difference in number of pigeons at the neutral site minus the hostile site. With n=32

measurements, the mean difference in number of pigeons is 3.9

with a standard deviation of 6.8

. Test to see if this provides evidence that the mean difference is greater than zero, meaning the pigeons can recognize faces (and hold a grudge!)

1Belguermi, A., ”Pigeons discriminate between human feeders,” Animal Cognition, 2011; 14: 909-914.

State the null and alternative hypotheses.

Give the test statistic and the p

-value.

Round your answer for the test statistic to two decimal places and the answer for the p

-value to three decimal places.

test statistic =

p

-value =

What is the conclusion of this test of hypotheses?

Do not reject H0

; we find evidence that pigeons can recognize faces.

Reject H0

; we find evidence that pigeons can recognize faces.

Do not reject H0

; we do not find evidence that pigeons can recognize faces.

Reject H0

; we do not find evidence that pigeons can recognize faces.

Chapter 6, Section 4-D, Exercise 180

Use the formula to find the standard error of the distribution of differences in sample means, x¯1-x¯2

.

Samples of size 120

from Population 1

with mean 81

and standard deviation 11

and samples of size 70

from Population 2

with mean 73

and standard deviation 17

Round your answer for the standard error to two decimal places.

standard error =

Enter your answer in accordance to the question statement

the absolute tolerance is +/-0.01

Chapter 6, Section 4-D, Exercise 184

Use a t

-distribution to answer this question. Assume the samples are random samples from distributions that are reasonably normally distributed, and that a t

-statistic will be used for inference about the difference in sample means. State the degrees of freedom used.

Find the endpoints of the t

-distribution with 2.5%

beyond them in each tail if the samples have sizes n1=14

and n2=25

.

Enter the exact answer for the degrees of freedom and round your answer for the endpoints to two decimal places.

degrees of freedom =

endpoints= ±

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November 29, 2020

November 29, 2020