A consumer agency is investigating the blowout pressures of Soap Stone tires. A Soap Stone tire is said to blow out when it separates from the wheel rim due to impact forces usually caused by hitting a rock or a pothole in the road. A random sample of 28 Soap Stone tires were inflated to the recommended pressure, and then forces measured in foot-pounds were applied to each tire (1 foot-pound is the force of 1 pound dropped from a height of 1 foot). The customer complaint is that some Soap Stone tires blow out under small-impact forces, while other tires seem to be well made and don't have this fault. For the 28 test tires, the sample standard deviation of blowout forces was 1358 foot-pounds.
Soap Stone claims its tires will blow out at an average pressure of 24,000 foot-pounds, with a standard deviation of 1020 foot-pounds. The average blowout force is not in question, but the variability of blowout forces is in question. Using a 0.01 level of significance, test the claim that the variance of blowout pressures is more than Soap Stone claims it is.
(i) Give the value of the level of significance.
State the null and alternate hypotheses.
H0: σ2 = 1,040,400; H1: σ2 > 1,040,400
H0: σ2 = 1,040,400; H1: σ2 <>
H0: σ2 = 1,040,400; H1: σ2 ≠ 1,040,400
H0: σ2 < 1,040,400;="" h1:="" σ2="">
(ii) Find the sample test statistic. (Round your answer to two decimal places.)
(iii) Find or estimate the P-value of the sample test statistic. (Round your answer to three decimal places.)
(iv) Conclude the test.
Since P-value ≥ α, we fail to reject the null hypothesis.
Since P-value < α,="" we="" reject="" the="" null="">
Since P-value < α,="" we="" fail="" to="" reject="" the="" null="">
Since P-value ≥ α, we reject the null hypothesis.
(v) Interpret the conclusion in the context of the application.
At the 1% level of significance, there is insufficient evidence to conclude that the variance is greater than claimed.
At the 1% level of significance, there is sufficient evidence to conclude that the variance is greater than claimed.