question #3 chapter 11

Some transportation experts claim that it is the variability of speeds, rather than the level of speeds, that is a critical factor in determining the likelihood of an accident occurring (Update, Virginia Department of Transportation, Winter 2000). One of the experts claims that driving conditions are dangerous if the variance of speeds exceeds 80 (mph)2. On a heavily traveled highway, a random sample of 61 cars revealed a mean and a variance of speeds of 57.5 mph and 88.7 (mph)2, respectively. Use Table 3.

a.Select the competing hypotheses to test the expert’s claim.   H0: σ2 ≤ 80; HA: σ2 > 80H0: σ2 ≥ 80; HA: σ2 < 80H0: σ2 = 80; HA: σ2 ≠ 80  b.

At the 5% significance level, find the critical value(s) and state the decision rule. (Round "" value and final answer to 3 decimal places.)

   Reject H0 if χ2df > .

c.Can you conclude that driving conditions are dangerous on this highway?   (Click to select)RejectDo not reject H0. At the 5% significance level, we (Click to select)cancannot conclude the variance of the speeds is greater than 80 mpg2.