Question

A social scientist suspects that the mean number of years of education for all adults in a large city is greater than 12 years. She will test her hypothesis using a random sample of 100 adults and finds the sample mean number of years is 12.98. Assume the standard deviation of the number of years of education for all adults is 3. State the appropriate null and alternative hypotheses.

From the previous problem, find the value of the test statistic.

From the previous problems, between what two p-values does your test statistic lie?

Answer 1

Given that,
population mean(u)=12
standard deviation, σ =3
sample mean, x =12.98
number (n)=100
null, Ho: μ=12
alternate, H1: μ>12
level of significance, α = 0.05
from standard normal table,right tailed z α/2 =1.645
since our test is right-tailed
reject Ho, if zo > 1.645
we use test statistic (z) = x-u/(s.d/sqrt(n))
zo = 12.98-12/(3/sqrt(100)
zo = 3.267
| zo | = 3.267
critical value
the value of |z α| at los 5% is 1.645
we got |zo| =3.267 & | z α | = 1.645
make decision
hence value of | zo | > | z α| and here we reject Ho
p-value : right tail - ha : ( p > 3.267 ) = 0.001
hence value of p0.05 > 0.001, here we reject Ho
ANSWERS
---------------
null, Ho: μ=12
alternate, H1: μ>12
test statistic: 3.267
critical value: 1.645
decision: reject Ho
p-value: 0.001
we have enough evidence to support the claim that A social scientist suspects that the mean number of years of education for all adults in a large city is greater than 12 years.