Answer:
Step-by-step explanation:
We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean
For the null hypothesis,
µ = 4.9
For the alternative hypothesis,
µ < 4.9
This is a left tailed test.
If the population variance is 0.36, the population standard deviation would be √0.36 = 0.6 psi
Since the population standard deviation is given, z score would be determined from the normal distribution table. The formula is
z = (x - µ)/(σ/√n)
Where
x = sample mean
µ = population mean
σ = population standard deviation
n = number of samples
From the information given,
µ = 4.9
x = 4.8
σ = 0.6
n = 210
z = (4.8 - 4.9)/(0.6/√210) = - 2.42
Looking at the normal distribution table, the probability corresponding to the z score is 0.0078
Since alpha, 0.1 > than the p value, 0.0078, then we would reject the null hypothesis. Therefore, there is sufficient evidence at the 0.1 level that the valve performs below the specifications.
