Question

Some traffic experts believe that the major cause of highway collisions is the differing speeds of cars. That is, when some cars are driven slowly while others are driven at speeds well in excess of the speed limit, cars tend to congregate in bunches, increasing the probability of accidents. Thus, the greater the variation in speeds, the greater will be the number of collisions that occur. Suppose that one expert believes that when the variance exceeds 19, the number of accidents will be unacceptably high. A random sample of the speeds of 100 cars on a highway with one of the highest accident rates in the country is taken. The sample mean speed was 105 km/hr with a sample variance of 22.32. Can we conclude at the 10% significance level that the variance in speeds exceeds the acceptable limit?

Answer 1

null hypothesis:     Ho:				σ2 =	19
Alternate hypothesis: Ha:				σ2 >	19

for sample size n:				=	100
s2				=	22.32

at 0.1 level and (n-1=99) df crtiical value=					117.407
Decision rule:reject Ho if test statistic F in critical region:				X2	>	117.407

test stat :

=χ2=(n-1)s2/σ2=

116.30

as test statistic is not higher then critical value we can not reject null hypothesis

we can not conclude at the 10% significance level that the variance in speeds exceeds the acceptable limit.