Conduct a Hypothesis test for mean comparison one-tail or two-tail (1 test on 2 main variables) on the information provided below.:
Sample 1: Mean: 29,264.10. Standard Deviation: 8,446.84. N=30.
19,400 |
24,380 |
32,500 |
25,400 |
34,395 |
19,500 |
23,570 |
30,930 |
32,000 |
29,000 |
34,000 |
36,800 |
45,000 |
39,500 |
41,830 |
45,000 |
35,800 |
35,950 |
40,000 |
26,810 |
26,995 |
23,710 |
17,999 |
19,000 |
26,000 |
24,000 |
12,875 |
31,000 |
18,000 |
26,579 |
Sample 2:
Mean: 57,640.83333. Standard Deviation: 29,995.85466. N=30
$48,950 |
$34,900 |
$102,600 |
$54,500 |
$33,900 |
$26,415 |
$39,785 |
$18,645 |
$22,995 |
$24,595 |
$30,750 |
$26,790 |
$66,500 |
$40,250 |
$89,900 |
$52,950 |
$75,150 |
$32,700 |
$113,900 |
$64,900 |
$54,600 |
$51,400 |
$113,900 |
$69,900 |
$49,700 |
$31,950 |
$54,900 |
$124,300 |
$91,100 |
$85,000 |
Unequal-variances t-test for mean comparison is the test we are told to use. Please list steps and calculations for the problem. Thank you so much!
Given that,
mean(x)=29264.1
standard deviation , s.d1=8446.84
number(n1)=30
y(mean)=57640.833
standard deviation, s.d2 =29995.85466
number(n2)=30
null, Ho: u1 = u2
alternate, H1: u1 != u2
level of significance, α = 0.05
from standard normal table, two tailed t α/2 =2.045
since our test is two-tailed
reject Ho, if to < -2.045 OR if to > 2.045
we use test statistic (t) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
to
=29264.1-57640.833/sqrt((71349105.9856/30)+(899751296.78384/30))
to =-4.988
| to | =4.988
critical value
the value of |t α| with min (n1-1, n2-1) i.e 29 d.f is 2.045
we got |to| = 4.98759 & | t α | = 2.045
make decision
hence value of | to | > | t α| and here we reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != -4.9876 )
= 0
hence value of p0.05 > 0,here we reject Ho
ANSWERS
---------------
null, Ho: u1 = u2
alternate, H1: u1 != u2
test statistic: -4.988
critical value: -2.045 , 2.045
decision: reject Ho
p-value: 0
we have enough evidence to support the claim that difference in
means between two samples.
Conduct a Hypothesis test for mean comparison one-tail or two-tail (1 test on 2 main variables)...