Question

A manufacturer of steel rods considers the process to be working properly if the mean length of the rods is 8.6 centimeters. The standard deviation of these rods always runs about 0.3 centimeters. The manufacturer would like to see if the process is working correctly by taking a random sample of n=64 . There is no indication of whether the rods may be too long or too short.

1. Establish H_o and H_a for this problem.
2. Determine the P-value if the sample yields an average length of 8.7 centimeters.
3. Interpret this P-value in a short paragraph.

Answer 1

Ans ) we have given Claim :  the mean length of the rods is 8.6 centimeters

population standard deviation = 0.3

n = 64

a ) let us consider null and alternate hypothesis

H0: $\mu = 8.6$

Ha : $\mu \neq 8.6$

b ) if sample mean = 8.7

$z = \frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}} }$

$z = \frac{8.7-8.6}{\frac{0.3}{\sqrt{64}} }$

z = 2.67

p-value is 0.008

c ) Since p-value is very small so we will reject H0 and conclude that we do not have sufficient evidence to accept the claim.

we conclude that   the mean length of the rods is not 8.6 centimeters