A consumer angency is investigating the blowout pressures of

A consumer angency 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 the impact forces usually caused by hitting a rock or a pothole in the road. A random sample of 2 Soap Stone tires were inflated to the recommended pressure, and then forces measured in foot-pounds were applied to each tire. 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 25 test tires, the sample standard deviation of blowout forces is 1350 foot-pounds.
Soap Stone claims its tires will blow out at an average pressure of 28,000 foot-pounds, with a standard deviation of 1025 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.
Classify the problem as being- F test for two variances, Chi-square test of homogeneity, Chi-square test of independence, Chi-square for testing or estimating sigma² or sigma, Chi-square goodness of fit
-Find the sample test statistic
-Find the P-value

Solution

F test for two variances

-Find the sample test statistic

F=s1^2/s2^2

=1350^2/1025^2

=1.73

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-Find the P-value

P-value= P(F with df1=n1-1=25-1=24, df2=n2-1=25-1=24 >1.73) =0.0933 (from F table)