Reference no: EM132967155

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 75 (mph)2. On a heavily traveled highway, a random sample of 54 cars revealed a mean and a variance of speeds of 62.5 mph and 95.1(mph)2, respectively. (You may find it useful to reference the appropriate table: chi-square table or F table)
a. Select the competing hypotheses to test if the variance of speeds exceeds 75 (mph)2.
H0: σ2 ≤ 75; HA: σ2 > 75
H0: σ2 ≥ 75; HA: σ2 < 75
H0: σ2 = 75; HA: σ2 ≠ 75

b-1. Find the p-value.
0.05 p-value < 0.10
0.025 p-value < 0.05
0.01 p-value < 0.025
p-value < 0.01
p-value 0.10

b-2. At the 10% significance level, can you conclude that driving conditions are dangerous on this highway?
Reject H0; we can conclude the variance of the speeds is greater than 75 mpg2.
Do not reject H0; we cannot conclude the variance of the speeds is greater than 75 mpg2.
Reject H0; we cannot conclude the variance of the speeds is greater than 75 mpg2.
Do not reject H0; we can conclude the variance of the speeds is greater than 75 mpg2.