Topic: Hypothesis Testing A company manufactures metal pipes of a standard lengt
ID: 3216918 • Letter: T
Question
Topic: Hypothesis Testing
A company manufactures metal pipes of a standard length, with the corresponding standard deviation of 1.2 cm. Recently it introduces a new machine for the production, and a random sample of 25 pipes is selected to measure the length. It is found that the sample standard deviation is 1 cm. The length of pipes is assumed to be approximately normally distributed. Using a 1% significance level, determine whether the new machine decreases the variation of the pipe length.
a) Let X be the length of a pipe produced by the new machine. What is the parameter of interest? Select one:
i. Mean of X,
ii. Variance of X, 2
iii. Sample mean, X¯
iv. Sample variance, S2
b) Decide the type of the hypothesis test. Select one:
i. Upper-tail test
ii. Lower-tail test
iii. Two-tail test
c) Decide the distribution used in the test. Select one:
i. t-distribution
ii. Normal distribution
iii. 2 distribution
d) Find the value of the test statistic (2 decimals).
e) Find the critical value (2 decimals).
f) What conclusion can we make? Select one:
i. It can be concluded that the new machine decreases the variation of the pipe length.
ii. It cannot be concluded that the new machine decreases the variation of the pipe length.
Explanation / Answer
Given that,
population standard deviation ()=1.2
sample standard deviation (s) =1
sample size (n) = 25
we calculate,
population variance (^2) =1.44
sample variance (s^2)=1
null, Ho: ^2 =1.44
alternate, H1 : ^2 <1.44
level of significance, = 0.01
from standard normal table,left tailed ^2 /2 =42.98
since our test is left-tailed
reject Ho, if ^2 o < -42.98
we use test statistic chisquare ^2 =(n-1)*s^2/o^2
^2 cal=(25 - 1 ) * 1 / 1.44 = 24*1/1.44 = 16.67
| ^2 cal | =16.67
critical value
the value of |^2 | at los 0.01 with d.f (n-1)=24 is 42.98
we got | ^2| =16.67 & | ^2 | =42.98
make decision
hence value of | ^2 cal | < | ^2 | and here we do not reject Ho
^2 p_value =0.8624
ANSWERS
---------------
lower tail test
2 distribution
null, Ho: ^2 =1.44
alternate, H1 : ^2 <1.44
test statistic: 16.67
critical value: -42.98
p-value:0.8624
decision: do not reject Ho
It cannot be concluded that the new machine decreases the variation of the pipe length