Question

According to the American Community Survey, the mean travel time to work in Collin County, Texas , in 2008 was 27.3 minutes. The Department of Transportation reprogrammed all the traffic lights in Collin County in an attempt to reduce travel time. To determine if there is evidence that travel time has decreased as a result of the reprogramming, the Department of Transportation obtains a random sample of 2500 commuters, records their travel time to work, and finds a sample mean of 27.0 minutes with a standard deviation of 8.5 mins. Does this result suggest that travel time has decreased at the 5% level of significance?

Answer 1

H0: $\mu$ >= 27.3

Ha: $\mu$ < 27.3

Test statistics

t = $\bar{x}$ - $\mu$ / S / sqrt(n)

= 27 - 27.3 / 8.5 / sqrt(2500)

= -1.76

t critical value at 0.05 level with 2499 df = -1.645

Since test statistics falls in rejection region, we have sufficient evidence to reject H0.

We conclude at 0.05 level that we have enough evidence to support the claim.