Question

13. We wish to see if, on average, traffic is moving at the posted speed limit of 65 miles per hour along a certain stretch of Interstate 70.  On each of four randomly selected days, a randomly selected car is timed and the speed of the car is recorded.  The observed speeds are 70, 65, 70, and 75 miles per hour. Assume σ= 4.08. Assuming that speeds are Normally distributed with mean µ, we test whether, on average, traffic is moving at 65 miles per hour, or at a speed significantly different than 65 miles per hour on average.

1. What are the null and alternative hypotheses?

2. Calculate the appropriate test statistic:

3. What’s the P-value for the test?

Answer 1

Solution :

=65

=70

=4.08

n = 4

This is the two tailed test .

The null and alternative hypothesis is ,

H0 :    = 65

Ha :     65

Test statistic = z

= ( - ) / / n

= (70-65) / 4.08 / 4

= 2.45

Test statistic = z = 2.45

P(z > 2.45) = 1 - P(z < 2.45 ) = 1 -0.9921  

P-value = 2 *0.0079 = 0.0158