Question

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A random sample of 89 tourists in Chattanooga showed that they spent an average of $2860 (in a week) with a standard deviation of $126; and a sample of 64 tourists in Orlando showed that they spent an average of $2935 (in a week) with a standard deviation of $138. We are interested in determining if there is any significant difference between the average expenditures of all the tourists who visited the two cities.

Determine the degrees of freedom for this test.

Select one:

a. 152

b. 128

c. 153

d. 127

Compute the test statistic.

Select one:

a. 0.157

b. -0.157

c. 3.438

d. -3.438

What is your conclusion? Let α = .05.

Select one:

a. Can not make a conclusion.

b. p-value > .05, can not reject H0.

c. p-value < .005, reject H0. There is a significant difference.

d. p-value < .05, reject H0. There is a significant difference.

Answer 1

Given that,
mean(x)=2860
standard deviation , s.d1=126
number(n1)=89
y(mean)=2935
standard deviation, s.d2 =138
number(n2)=64
null, Ho: u1 = u2
alternate, H1: u1 != u2
level of significance, α = 0.05
from standard normal table, two tailed t α/2 =1.998
since our test is two-tailed
reject Ho, if to < -1.998 OR if to > 1.998
we use test statistic (t) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =2860-2935/sqrt((15876/89)+(19044/64))
to =-3.438
| to | =3.438
critical value
the value of |t α| with min (n1-1, n2-1) i.e 63 d.f is 1.998
we got |to| = 3.43782 & | t α | = 1.998
make decision
hence value of | to | > | t α| and here we reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != -3.4378 ) = 0.001
hence value of p0.05 > 0.001,here we reject Ho
ANSWERS
---------------
null, Ho: u1 = u2
alternate, H1: u1 != u2
the degrees of freedom for this test.
option: A.
test statistic: -3.438
option:D
critical value: -1.998 , 1.998
decision: reject Ho
p-value: 0.001
option:D
. p-value < .05, reject H0. There is a significant difference
we have enough evidence to support the claim that difference between the average expenditures of all the tourists who visited the two cities