Question

Kyle is studying migration patterns of birds. Specifically, he is comparing the distance travelled by geese and the distance travelled by pelicans in a year. Do geese travel significantly more distance than pelicans do?

Geese Pelicans
M = 191 miles M = 190 miles
n = 61 n = 61
s = 1.429 s = 1.355

Required:
a. State the null and alternative hypotheses in words.
b. Locate the critical value that defines the critical region.
c. Calculate your statistic.
d. Make a decision with respect to the null.
e. Write a concluding statement in everyday language.

Answer 1

H0 : μ1 - μ2 = 0

H0 : μ1 - μ2 > 0

Test statistic = 3.96

Critical value = 1.67

Reject H0

We can conclude that there is significant evidence to support the claim that geese do travel more Than pelicans

Explanation:

M= xbar1 = 191 ; M = xbar2 = 190 miles

n1 = 61 n2 = 61

s = 1.429 ; s2 = 1.355

Hypothesis :

H0 : μ1 - μ2 = 0

H0 : μ1 - μ2 > 0

Test statistic :

(x1 - x2) ÷ √[(s1²/n1) + (s2²/n2)]

(191 - 190) ÷ √[(1.429²/61) + (1.355²/61)]

1 ÷ √[(0.0334760) + (0.0300987)]

1 ÷ √0.0635747

1 ÷ 0.2521402

= 3.966

Degree of freedom :

df = n - 1

df = 61 - 1 = 60

Critical value :

Tcritical at 0.05%, df = 60

Tcritical = 1.67

Decision region:

Reject H0 if Tstatistic > Tcritical

Since ;

3.96 > 1.67 ; We reject H0

We can conclude that there is significant evidence to support the claim that geese do travel more Than pelicans