Question

A package of a certain type of cookies claims that there are about 11 grams of sugar in a single cookie. Evaluate the validity of this claim based on a sample of 14 randomly chosen cookies which had the mean value of 11.2g of sugar with standard deviation 0.3g. Use α = 0.05 significance level

Answer 1

Given that,
population mean(u)=11
sample mean, x =11.2
standard deviation, s =0.3
number (n)=14
null, Ho: μ=11
alternate, H1: μ!=11
level of significance, α = 0.05
from standard normal table, two tailed t α/2 =2.16
since our test is two-tailed
reject Ho, if to < -2.16 OR if to > 2.16
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =11.2-11/(0.3/sqrt(14))
to =2.4944
| to | =2.4944
critical value
the value of |t α| with n-1 = 13 d.f is 2.16
we got |to| =2.4944 & | t α | =2.16
make decision
hence value of | to | > | t α| and here we reject Ho
p-value :two tailed ( double the one tail ) - Ha : ( p != 2.4944 ) = 0.0269
hence value of p0.05 > 0.0269,here we reject Ho
ANSWERS
---------------
null, Ho: μ=11
alternate, H1: μ!=11
test statistic: 2.4944
critical value: -2.16 , 2.16
decision: reject Ho
p-value: 0.0269
we have enough evidence to support the claim that A package of a certain type of cookies claims that there are about 11 grams of sugar in a single cookie.