Question

If you wanted to test a hypothesis that a sample of 75 people have a mean similar to a population with a mean of 115 (using a One-Sample T-Test in SPSS), the Test Value would be:

Answer 1

Assume data,
sample mean, x =110
standard deviation, s =18.48

Given that,
population mean(u)=115
number (n)=75
null, Ho: μ=115
alternate, H1: μ!=115
level of significance, α = 0.05
from standard normal table, two tailed t α/2 =1.993
since our test is two-tailed
reject Ho, if to < -1.993 OR if to > 1.993
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =110-115/(18.48/sqrt(75))
to =-2.3431
| to | =2.3431
critical value
the value of |t α| with n-1 = 74 d.f is 1.993
we got |to| =2.3431 & | t α | =1.993
make decision
hence value of | to | > | t α| and here we reject Ho
p-value :two tailed ( double the one tail ) - Ha : ( p != -2.3431 ) = 0.0218
hence value of p0.05 > 0.0218,here we reject Ho
ANSWERS
---------------
null, Ho: μ=115
alternate, H1: μ!=115
test statistic: -2.3431
critical value: -1.993 , 1.993
decision: reject Ho
p-value: 0.0218
we have enough evidence to support the claim that mean similar to a population with a mean of 115.