Question

In the normal habitat, pigeons are 11.9 inches high, A study about urban pigeons wants to find out if the urban ones are smaller or larger. The height of pigeons is normal distributed. 20 pigeons were captured and measured and their mean height is 12.4 inches with a standard deviation of 1.2 inches. Do the urban pigeons have a different mean height than the wild ones? α = 0.02

(a) What are the null and alternative hypotheses?
(b) What is the test statistic?
(c) What is the critical value or p value?
(d) Do you reject or fail to reject the null hypothesis? Explain your reasoning.
(e) Conclusion?

Answer 1

Solution:

a)

The null and alternative hypothesis are

H₀ : = 11.9 vs H_a :    11.9

b)

The test statistic t is

t =   = [12.4 - 11.9]/[1.2/20] = 1.863

Test statistic t = 1.863

c)

n = 20

df = n - 1 = 20 - 1 = 19

sign in H1 indicates that the test is "TWO TAILED"

t = 1.863

p value = 0.078

d)

fail to reject the null hypothesis

Because the p value is greater than the significance level α = 0.02

e)

There is not sufficient evidence to conclude that urban pigeons have a different mean height than the wild ones.