Answer:
Step-by-step explanation:
Hello!
The variable of interest is:
X: Impact force needed for Sap Stone tires to blow out. (foot-pounds)
n= 29, S= 1358 foot-pound
a)
Soap Stone claims that "The tires will blow out at an average pressure of μ= 26000 foot-pounds with a standard deviation of σ= 1020 foot-pounds.
According to the consumer's complaint, the variability of the blown out forces is greater than the value determined by the company.
I)
Then the parameter of interest is the population variance (or population standard deviation) and to test the consumer's complaint you have to conduct a Chi-Square test for σ².
σ²= (1020)²= 1040400 foot-pounds²
H₀: σ² ≤ 1040400
H₁: σ² > 1040400
α: 0.01
II)
III)
This test is one-tailed to the right and so is the p-value. This distribution has n-1= 29-1= 28 degrees of freedom, so you can calculate the p-value as:
P(X²₂₈≥49.63)= 1 - P(X²₂₈<49.63)= 1 - 0.99289= 0.00711
⇒ The p-value is less than the significance level so the test is significant at 1%. You can conclude that the population variance of the blowout forces is less than 1040400 foot-pounds², at the same level the population standard deviation of the blow out forces is less than 1020 foot-pounds.
b)
99% CI for the variance. Using the X² statistic you can calculate it as:
[1041312.253; 3935415.898] foot-pounds²
I hope this helps!