Question

Below is a sample of 12 flights with their domestic airfares shown for both years. Current year 378,351,249,588,525,294. Previous year 549,447,522,684,309,390. Current year 468,333,513,600,468,669. Previous year 573,348,564,399,255,363. a. Formulate the hypotheses and test for a significant increase in the mean domestic airfare for business travel for the one-year period. (less than, greater than, less or equal, greater or equal etc...) t value? (3 decimals degrees of freedom? p-value? Using a .05 level of significance, what is your conclusion? b. What is the sample mean domestic airfare for business travel for each year? current year___? 2 decimals previous year___? 2 decimals c. What is the percentage change in the airfare for the one-year period?

Answer 1

Given that,
mean(x)=453
standard deviation , s.d1=132.4764
number(n1)=12
y(mean)=450.25
standard deviation, s.d2 =127.9042
number(n2)=12
null, Ho: u1 = u2
alternate, H1: u1 != u2
level of significance, α = 0.05
from standard normal table, two tailed t α/2 =2.201
since our test is two-tailed
reject Ho, if to < -2.201 OR if to > 2.201
we use test statistic (t) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =453-450.25/sqrt((17549.99656/12)+(16359.48438/12))
to =0.052
| to | =0.052
critical value
the value of |t α| with min (n1-1, n2-1) i.e 11 d.f is 2.201
we got |to| = 0.05173 & | t α | = 2.201
make decision
hence value of |to | < | t α | and here we do not reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != 0.0517 ) = 0.96
hence value of p0.05 < 0.96,here we do not reject Ho
ANSWERS
---------------
a.
null, Ho: u1 = u2
alternate, H1: u1 != u2
test statistic: 0.052
critical value: -2.201 , 2.201
decision: do not reject Ho
p-value: 0.96
we do not have enough evidence to support the claim that domestic air fairs difference between current year and previous year
b.
sample mean of current year air fair is 453
sample mean of previous year air fairs is 450.25
c.
the percentage change in the airfare for the one-year period is 96%