Coffec packages indicate a content of 500g. A fraud prevention inspector wants t

Question

Coffec packages indicate a content of 500g. A fraud prevention inspector wants to chock that the packages do contain at least 500g on average. Otherwise, he will prosecute the coffee brand. He runs a t-test with significance level -1%. 1. Define the hypotheses Ho and Ha he takes. 2. (a) Describe what type I crror is in gencral, and what it would mcan in this casc. (b) Assuming that the coffee packages do actually weigh 500g on average, what is the probability that the inspector rejects Ho? standard deviation of 20g. What is his conclusion? Explain.

Explanation / Answer

Q1.
null,the package do cotain atleast 500 grams, Ho: >=500
alternate, package contains less than 500 grams, H1: <500

Q2.
Type I error explains that rejecting the null hypothesis when it
is actually true, and for the current instance it is pacakge contains
less than 500 grams since the actual made has atleast 500 grams

Q3.
Given that,
population mean(u)=500
sample mean, x =495
standard deviation, s =20
number (n)=41
null, Ho: >=500
alternate, H1: <500
level of significance, = 0.01
from standard normal table,left tailed t /2 =2.423
since our test is left-tailed
reject Ho, if to < -2.423
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =495-500/(20/sqrt(41))
to =-1.6008
| to | =1.6008
critical value
the value of |t | with n-1 = 40 d.f is 2.423
we got |to| =1.6008 & | t | =2.423
make decision
hence value of |to | < | t | and here we do not reject Ho
p-value :left tail - Ha : ( p < -1.6008 ) = 0.05865
hence value of p0.01 < 0.05865,here we do not reject Ho
ANSWERS
---------------
null, Ho: >=500
alternate, H1: <500
test statistic: -1.6008
critical value: -2.423
decision: do not reject Ho
p-value: 0.05865

we have evidence to support that the pacakge contains atleast 500 grams

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