A consumer agency is investigating the blowout pressures of SoapStone tires. A Soap Stone tire is said to blow out when itseparates from the wheel rim due to impact forces usually caused byhitting a rock or a pothole in the road. A random sample of 28 SoapStone tires were inflated to the recommended pressure, and thenforces measured in foot-pounds were applied to each tire (1foot-pound is the force of 1 pound dropped from a height of 1foot). The customer complaint is that some Soap Stone tires blowout under small-impact forces, while other tires seem to be wellmade and don't have this fault. For the 28 test tires, the samplestandard deviation of blowout forces was 1356 foot-pounds.

(a) Soap Stone claims its tires will blow out at an averagepressure of 20,000 foot-pounds, with a standard deviation of 1026foot-pounds. The average blowout force is not in question, but thevariability of blowout forces is in question. Using a 0.1 level ofsignificance, test the claim that the variance of blowout pressuresis more than Soap Stone claims it is.

Classify the problem as being a Chi-square test of independence orhomogeneity, Chi-square goodness-of-fit, Chi-square for testing orestimating σ² or σ, F testfor two variances, One-way ANOVA, or Two-way ANOVA, then performthe following.

One-way ANOVAF test for twovariances     Chi-square test ofindependenceChi-square for testing or estimatingσ² or σChi-square test ofhomogeneityChi-square goodness-of-fitTwo-way ANOVA

(i) Give the value of the level of significance.

State the null and alternate hypotheses.

H_o: σ² = 1052676;H₁: σ² >1052676H_o: σ² = 1052676;H₁: σ² ≠1052676     H_o:σ² < 1052676; H₁:σ² = 1052676H_o:σ² = 1052676; H₁:σ² < 1052676

(ii) Find the sample test statistic. (Use two decimalplaces.)


(iii) Find the P-value of the sample test statistic. (Usefour decimal places.)

(iv) Conclude the test.

Since the P-value is greater than or equal to the levelof significance α = 0.10, we fail to reject the nullhypothesis.Since the P-value is less than the level ofsignificance α = 0.10, we reject the nullhypothesis.     Since the P-valueis less than the level of significance α = 0.10, we failto reject the null hypothesis.Since the P-value is greaterthan or equal to the level of significance α = 0.10, wereject the null hypothesis.

(v) Interpret the conclusion in the context of the application.

At the 10% level of significance, there is insufficient evidenceto conclude that the variance is not greater than claimed.At the10% level of significance, there is sufficient evidence to concludethat the variance is greater thanclaimed.     At the 10% level ofsignificance, there is sufficient evidence to conclude that thevariance is not greater than claimed.At the 10% level ofsignificance, there is sufficient evidence to conclude that thevariance is greater than claimed.

(b) Find a 90% confidence interval for the variance of blowoutpressures, using the information from the random sample. (Use onedecimal place.)
< σ² <  square foot-pounds