Question

To test the claim that each muffin contains at least 9 nuts, a sample of 16 muffins is taken . The average number of nuts per muffin in the sample was 8 with a sample standard deviation of 3. Assume the distribution of the population is normal. Calculate the p-value. Show your answer to four decimal places.

Answer 1

Given that,
population mean(u)=9
sample mean, x =8
standard deviation, s =3
number (n)=16
null, Ho: μ<=9
alternate, H1: μ>=9
level of significance, α = 0.05
from standard normal table,right tailed t α/2 =1.753
since our test is right-tailed
reject Ho, if to > 1.753
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =8-9/(3/sqrt(16))
to =-1.3333
| to | =1.3333
critical value
the value of |t α| with n-1 = 15 d.f is 1.753
we got |to| =1.3333 & | t α | =1.753
make decision
hence value of |to | < | t α | and here we do not reject Ho
p-value :right tail - Ha : ( p > -1.3333 ) = 0.89884
hence value of p0.05 < 0.89884,here we do not reject Ho
ANSWERS
---------------
null, Ho: μ<=9
alternate, H1: μ>=9
test statistic: -1.3333
critical value: 1.753
decision: do not reject Ho
p-value: 0.89884
we do not have enough evidence to support the claim that each muffin contains at least 9 nuts.