In: Statistics and Probability
An owner of press is claiming that the standard deviation of the pressure is less than 10 pounds-per-square-inch (psi). Suppose you take a random sample of 15 measurements throughout the day of the psi and find the mean is 5 and standard deviation to be 14, using the α=0.05, test the claim by traditional approach.
H0: Null Hypothesis: 10 ( the standard deviation of the pressure is not less than 10 pounds-per-square-inch (psi).
HA: Alternative Hypothesis: < 10 ( the standard deviation of the pressure is less than 10 pounds-per-square-inch (psi). (Claim)
n = 15
s = 14
= 0.05
df = 15 - 1 = 14
By Technology, critical value of = 6.571
Test Statistic is given by:
Since calculated value of = 27.44 is greater than critical value of = 6.571, the difference is not significant. Fail to reject null hypothesis.
Conclusion:
The data do not support the claim that the standard deviation of
the pressure is less than 10 pounds-per-square-inch (psi).