Lazurus Steel Corporation produces iron rods that are supposed to be 36 inches l

Question

Lazurus Steel Corporation produces iron rods that are supposed to be 36 inches long. The machine that makes these rods does not produce each rod exactly 36 inches long. The lengths of the rods are normally distributed and vary slightly. It is known that when the machine is working properly, the mean length of the rods is 36 inches. The standard deviation of the lengths of all rods produced on this machine is always equal to 0.035 inch. The quality control department at the company takes a sample of 20 such rods every week, calculates the mean length of these rods, and tests the null hypothesis, =36 inches, against the alternative hypothesis, 36 inches. If the null hypothesis is rejected, the machine is stopped and adjusted. A recent sample of 20 rods produced a mean length of 36.015 inches.

Calculate the p-value for this test of hypothesis. Based on this p-value, will the quality control inspector decide to stop the machine and adjust it if he chooses the maximum probability of a Type I error to be 0.05?

Use the normal distribution table. Round your answer to four decimal places.

The machine needs or does not need adjustment?

Explanation / Answer

Given that,
population mean(u)=36
standard deviation, =0.035
sample mean, x =36.015
number (n)=20
null, Ho: =36
alternate, H1: !=36
level of significance, = 0.05
from standard normal table, two tailed z /2 =1.96
since our test is two-tailed
reject Ho, if zo < -1.96 OR if zo > 1.96
we use test statistic (z) = x-u/(s.d/sqrt(n))
zo = 36.015-36/(0.035/sqrt(20)
zo = 1.92
| zo | = 1.92
critical value
the value of |z | at los 5% is 1.96
we got |zo| =1.92 & | z | = 1.96
make decision
hence value of |zo | < | z | and here we do not reject Ho
p-value : two tailed ( double the one tail ) - ha : ( p != 1.92 ) = 0.06
hence value of p0.05 < 0.06, here we do not reject Ho
ANSWERS
---------------
null, Ho: =36
alternate, H1: !=36
test statistic: 1.92
critical value: -1.96 , 1.96
decision: do not reject Ho
p-value: 0.06

we dont have evidence to support the claim

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