Question

A random sample of 4 college students was drawn from a large university. Their ages are 22, 17, 23, and 20 years.

a) Test to determine if we can infer at the 5% significance level that the population mean is not equal to 20.

b) Interpret your conclusion.

Answer 1

Given that,
population mean(u)=20
sample mean, x =20.5
standard deviation, s =2.6458
number (n)=4
null, Ho: μ=20
alternate, H1: μ!=20
level of significance, α = 0.05
from standard normal table, two tailed t α/2 =3.182
since our test is two-tailed
reject Ho, if to < -3.182 OR if to > 3.182
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =20.5-20/(2.6458/sqrt(4))
to =0.378
| to | =0.378
critical value
the value of |t α| with n-1 = 3 d.f is 3.182
we got |to| =0.378 & | t α | =3.182
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 != 0.378 ) = 0.7306
hence value of p0.05 < 0.7306,here we do not reject Ho
ANSWERS
---------------
a.
null, Ho: μ=20
alternate, H1: μ!=20
test statistic: 0.378
critical value: -3.182 , 3.182
decision: do not reject Ho
p-value: 0.7306
b.
we do not have enough evidence to support the claim that the population mean is not equal to 20.