Show all work: we sample 40 items from a population whose standard deviation is
ID: 3220453 • Letter: S
Question
Show all work:
we sample 40 items from a population whose standard deviation is 15 and test, at the .05 level, the claim that the population mean is less than 80. Find the probability of committing a type II error if, in reality, the population mean is 82. Also, find the power of the test
A large corporation claims that the estimated time it takes their trucks to get from the manufacturing plant to the individual stores is 95 minutes. A random sample 50 trucks showed that the average time was 100 minutes with a standard deviation of 20 minutes. Conduct an appropriate test to prove that the claim is too low at a 0.10 level of significance and find the p-value.
Explanation / Answer
Given that,
population mean(u)=95
sample mean, x =100
standard deviation, s =20
number (n)=50
null, Ho: µ=95
alternate, H1: µ>95
level of significance, a = 0.1
from standard normal table,right tailed t a/2 =1.299
since our test is right-tailed
reject Ho, if to > 1.299
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =100-95/(20/sqrt(50))
to =1.768
| to | =1.768
critical value
the value of |t a| with n-1 = 49 d.f is 1.299
we got |to| =1.768 & | t a | =1.299
make decision
hence value of | to | > | t a| and here we reject Ho
p-value :right tail - Ha : ( p > 1.7678 ) = 0.04166
hence value of p0.1 > 0.04166,here we reject Ho
ANSWERS
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null, Ho: µ=95
alternate, H1: µ>95
test statistic: 1.768
critical value: 1.299
decision: reject Ho
p-value: 0.04166