Question

Test this hypothesis at the .04 significance level. Assume a random sample.

Data: 0,0,0,1,1,1,1,1,1,2,2,3

Answer 1

Assumed population mean(u)=1 because not given in the data
Given that,
sample mean, x =1.0833
standard deviation, s =0.9003
number (n)=12
null, Ho: μ=1
alternate, H1: μ!=1
level of significance, α = 0.04
from standard normal table, two tailed t α/2 =2.328
since our test is two-tailed
reject Ho, if to < -2.328 OR if to > 2.328
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =1.0833-1/(0.9003/sqrt(12))
to =0.321
| to | =0.321
critical value
the value of |t α| with n-1 = 11 d.f is 2.328
we got |to| =0.321 & | t α | =2.328
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 != 0.3205 ) = 0.7546
hence value of p0.04 < 0.7546,here we do not reject Ho
ANSWERS
---------------
null, Ho: μ=1
alternate, H1: μ!=1
test statistic: 0.321
critical value: -2.328 , 2.328
decision: do not reject Ho
p-value: 0.7546
we do not have enough evidence to support the claim that population mean is 1.