Question

Two samples will almost always be different – even if they were selected from the same population. Inferential statistics helps us determine if that difference is real and will be consistently seen or if it is due to chance. Design an “experiment” or “study” that measures something (ratio scale or interval scale) in two samples. Each sample must have at least 20 data points (n = 20 or more). Run an independent t-test or related t-test to determine if there is a significant difference between the two samples. SHOW YOUR WORK

Answer 1

Two samples will almost always be different – even if they were selected from the same population.
Design an experiment or studythat measures something (ratio scale or interval scale) in two samples.
Each sample must have at least 20 data points (n = 20 or more). Run an independent t-test or related t-test
Assumed values for two different samples and their means and standard deviations,
mean(x)=5.966
standard deviation , s.d1=3.547
number(n1)=25
y(mean)=4.333
standard deviation, s.d2 =2.604
number(n2)=25
null, Ho: u1 = u2
alternate, H1: u1 != u2
level of significance, α = 0.05
from standard normal table, two tailed t α/2 =2.064
since our test is two-tailed
reject Ho, if to < -2.064 OR if to > 2.064
we use test statistic (t) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =5.966-4.333/sqrt((12.58121/25)+(6.78082/25))
to =1.856
| to | =1.856
critical value
the value of |t α| with min (n1-1, n2-1) i.e 24 d.f is 2.064
we got |to| = 1.85558 & | t α | = 2.064
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 != 1.8556 ) = 0.076
hence value of p0.05 < 0.076,here we do not reject Ho
ANSWERS
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null, Ho: u1 = u2
alternate, H1: u1 != u2
test statistic: 1.856
critical value: -2.064 , 2.064
decision: do not reject Ho
p-value: 0.076
we do not have enough evidence to support the claim that if there is a significant difference between the two samples