Answer:
The valves perform above expectations.
Step-by-step explanation:
We are given the following information in the question:
Population mean, μ = 7.6 pounds per square inch
Sample size, n = 140
Sample mean,
= 7.8 pounds per square inch
Population standard deviation = 1.0 pounds per square inch
Level of significance = 0.05
We design the null and alternate hypothesis:
: μ = 7.6 pounds per square inch
: μ > 7.6 pounds per square inch
Formula:
![z_{stat} = \displaystyle\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}}}](https://tex.z-dn.net/?f=z_%7Bstat%7D%20%3D%20%5Cdisplaystyle%5Cfrac%7B%5Cbar%7Bx%7D-%5Cmu%7D%7B%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D%7D)
![z_{stat} = \displaystyle\frac{7.8-7.6}{\frac{1}{\sqrt{140}}}](https://tex.z-dn.net/?f=z_%7Bstat%7D%20%3D%20%5Cdisplaystyle%5Cfrac%7B7.8-7.6%7D%7B%5Cfrac%7B1%7D%7B%5Csqrt%7B140%7D%7D%7D)
![z_{stat} = 2.366](https://tex.z-dn.net/?f=z_%7Bstat%7D%20%3D%202.366)
Now, we are performing a one tail test with level of significance of 0.05, we calculate the critical value of z with the help of standard normal distribution table.
Thus,
= 1.645
Result:
Since, ![z_{stat} > z_{critical}](https://tex.z-dn.net/?f=z_%7Bstat%7D%20%3E%20z_%7Bcritical%7D)
is rejected.
Thus, we accept the alternate hypothesis.
Hence, the valve perform above expectations.