Question

A psychologist interested in examining workplace stress recruits 30 adults and administered a stress questionnaire to them. The questionnaire’s scores ranged from 0-20 with lower scores indicating lower amounts of stress and higher scores indicating significant amounts of stress. On average, workers tend to score a 10. Results from this questionnaire showed workers at this company on average scored 15 with a standard deviation estimate of 3.96. Test the viability that µ = 10 using a one-sample t-test

Answer 1

Given that,
population mean(u)=10
sample mean, x =15
standard deviation, s =3.96
number (n)=30
null, Ho: μ=10
alternate, H1: μ!=10
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-u/(s.d/sqrt(n))
to =15-10/(3.96/sqrt(30))
to =6.916
| to | =6.916
critical value
the value of |t α| with n-1 = 29 d.f is 2.045
we got |to| =6.916 & | 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 != 6.9157 ) = 0
hence value of p0.05 > 0,here we reject Ho
ANSWERS
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null, Ho: μ=10
alternate, H1: μ!=10
test statistic: 6.916
critical value: -2.045 , 2.045
decision: reject Ho
p-value: 0
we have enough evidence to support the claim that On average, workers tend to score a 10.