Question

Carleton Chemical claims that they can produce more than 800 tons of benzene on average per week. A random sample of 36 weeks of production yields a mean and SD as follows: x ̅=823 and s = 79.8. At the = .05 significance level, does the sample data provide significant evidence to support the claim made by the Carleton Company?

a) Set up hypotheses Ho and Ha to test the company’s claim.

Go to STAT >> TESTS, and choose T-test – select the STATS option and enter the given sample information.

b) State the test statistic and p-value given by the calculator.

c) Compare the p-value to  = .05. State the appropriate decision (either Reject Ho or Fail to reject Ho), along with an explanation.

d) Interpret this decision to write a conclusion for the test.

Answer 1

Given that,
population mean(u)=800
sample mean, x =823
standard deviation, s =79.8
number (n)=36
null, Ho: μ=800
alternate, H1: μ>800
level of significance, α = 0.05
from standard normal table,right tailed t α/2 =1.69
since our test is right-tailed
reject Ho, if to > 1.69
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =823-800/(79.8/sqrt(36))
to =1.7293
| to | =1.7293
critical value
the value of |t α| with n-1 = 35 d.f is 1.69
we got |to| =1.7293 & | t α | =1.69
make decision
hence value of | to | > | t α| and here we reject Ho
p-value :right tail - Ha : ( p > 1.7293 ) = 0.04628
hence value of p0.05 > 0.04628,here we reject Ho
ANSWERS
---------------
a.
null, Ho: μ=800
alternate, H1: μ>800
b.
test statistic: 1.7293
critical value: 1.69
decision: reject Ho
c.
p-value: 0.04628
d.
we have enough evidence to support the claim that they can produce more than 800 tons of benzene on average per week.