Part b): I would personally use a Z-test for this, because our standard deviatio
ID: 3334181 • Letter: P
Question
Part b): I would personally use a Z-test for this, because our standard deviation(sigma) is given, but another solution suggests a T-test. Please tell me your thoughts on this.
2.16. The breaking strength of a fiber is required to be at least 150 psi. Past experience has indicated that the standard deviation of breaking strength is 3 psi. A random sample of four specimens is tested, and the results are y 145, y,- 153, y- 150, and y4-147 (a) State the hypotheses that you think should be tested in this experiment.Explanation / Answer
Given that,
population mean(u)=150
standard deviation, =3
sample mean, x = (145+153+150+147)/4 = 148.75
number (n)=4
null, Ho: =150
alternate, H1: <150
level of significance, = 0.05
from standard normal table,left tailed z /2 =1.645
since our test is left-tailed
reject Ho, if zo < -1.645
we use test statistic (z) = x-u/(s.d/sqrt(n))
zo = 148.75-150/(3/sqrt(4)
zo = -0.83333
| zo | = 0.83333
critical value
the value of |z | at los 5% is 1.645
we got |zo| =0.83333 & | z | = 1.645
make decision
hence value of |zo | < | z | and here we do not reject Ho
p-value : left tail - ha : ( p < -0.83333 ) = 0.20233
hence value of p0.05 < 0.20233, here we do not reject Ho
ANSWERS
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null, Ho: =150
alternate, H1: <150
test statistic: -0.83333
critical value: -1.645
decision: do not reject Ho
p-value: 0.20233
this should be tested in this experiment