Researchers in Australia set up an experiment to test whether walking dogs withi

Question

Researchers in Australia set up an experiment to test whether walking dogs within parks significantly affected the number of birds in the park*. Their treatments consisted of 1) humans walking dogs on a leash; 2) humans walking without dogs, 3) no walkers at all [a no-disturbance control]. Ten minutes after the trial, researchers counted the number of birds observed nearby.   Here is what they found:

Disturbance type

Mean # birds per site

SD

n

None (Control)

10.1

2.74

28

Humans only

9.7

3.25

30

Humans with dogs

7.3

3.52

30

Assume the data are normally distributed with equal variances. Answer the following questions as part of the process.

1. What is the null hypothesis to be tested?

H0: All three groups have same population mean number of birds.

2. What is the alternative hypothesis? (0.5 pts)

3. Analyze these data and test whether there is a significant difference among the groups. Calculate the missing quantities in the table below. To receive full points, you must show your work.

Source

SS

df

MS

F

Disturbance type

Error

NA

Total

NA

NA

Disturbance type

Mean # birds per site

SD

n

None (Control)

10.1

2.74

28

Humans only

9.7

3.25

30

Humans with dogs

7.3

3.52

30

Explanation / Answer

1) H0: All three groups have same population mean number of birds.

2) alternative hypothesis"Ha: at least one group has different mean number of birds.

3)

as p value is very less we reject null hypothesis and conclude that  at least one group has different mean number of birds.

i ni Xi Si^2 ni*(Xi- grand mean)^2 (ni-1)*Si^2 nose 28 10.1 7.508 33.322 202.705 human 30 9.7 10.563 14.321 306.313 human with dogs 30 7.3 12.390 87.630 359.322 Weighted mean 9.009 135.273 868.339 SSG SSE Source of variation SS df MS F P value treatment 135.273 2 67.636 6.621 0.0021 error 868.339 85 10.216 total 1003.612 87

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