Question

Expedia would like to test the hypothesis that the average roundtrip airfare between Philadelphia and Paris is higher for a flight originating in Philadelphia when compared to a flight originating in Paris. The following data summarizes the sample statistics for roundtrip flights originating in both cities. Assume that the population variances are equal.

	Originating City
	Philadelphia	Paris
Sample mean	$1,240	$1,060
Sample size	15	19
Sample standard deviation	$270	$240

A) If Population 1 is defined as flights originating in Philadelphia and Population 2 is defined as flights originating in Paris, the correct hypothesis statement for this hypothesis test would be

		H0: μ1 - μ2 = 0; H1: μ1 - μ2 < 0
		H0: μ1 - μ2 = 0; H1: μ1 - μ2 > 0
		H0: μ1 - μ2 = 0; H1: μ1 - μ2 ≠ 0
		H0: 2 - 1 = 0; H1: 2 - 1 > 0.

B) If Population 1 is defined as flights originating in Philadelphia and Population 2 is defined as flights originating in Paris, the degrees of freedom for this hypothesis test are ________.

		32
		33
		28
		34

Answer 1

Given that,
mean(x)=1240
standard deviation , s.d1=270
number(n1)=15
y(mean)=1060
standard deviation, s.d2 =240
number(n2)=19
null, Ho: u1 = u2
alternate, H1: u1 > u2
level of significance, α = 0.05
from standard normal table,right tailed t α/2 =1.694
since our test is right-tailed
reject Ho, if to > 1.694
calculate pooled variance s^2= (n1-1*s1^2 + n2-1*s2^2 )/(n1+n2-2)
s^2 = (14*72900 + 18*57600) / (34- 2 )
s^2 = 64293.75
we use test statistic (t) = (x-y)/sqrt(s^2(1/n1+1/n2))
to=1240-1060/sqrt((64293.75( 1 /15+ 1/19 ))
to=180/87.579
to=2.055
| to | =2.055
critical value
the value of |t α| with (n1+n2-2) i.e 32 d.f is 1.694
we got |to| = 2.055 & | t α | = 1.694
make decision
hence value of | to | > | t α| and here we reject Ho
p-value: right tail -ha : ( p > 2.0553 ) = 0.02404
hence value of p0.05 > 0.02404,here we reject Ho
ANSWERS
---------------
A.
null, Ho: u1 = u2
alternate, H1: u1 > u2
test statistic: 2.055
B.
degree of freedom = 32
critical value: 1.694
decision: reject Ho
p-value: 0.02404
we have enough evidence to supportthe claim that the average roundtrip airfare between Philadelphia and Paris is higher for a flight originating in Philadelphia when compared to a flight originating in Paris.