Question

Every road has one at some point - construction zones that have much lower speed limits. To see if drivers obey these lower speed limits, a police officer uses a radar gun to measure the speed (in miles per hours, or mph) of a random sample of 10 drivers in a 25 mph construction zone. Here are the data: 27; 33; 32; 21; 30; 30; 29; 25; 27; 34. Is there convincing evidence that at the α=0.01 significance level that the average speed of drivers in this construction zone is greater than the posted speed limit?

Answer 1

Solution:

x	x2
27	729
33	1089
32	1024
21	441
30	900
30	900
29	841
25	625
27	729
34	1156
∑x=288	∑x2=8434

Mean ˉx=∑xn

=27+33+32+21+30+30+29+25+27+34/10

=288/10

=28.8


Sample Standard deviation S=√∑x2-(∑x)2nn-1

=√8434-(288)210/9

=√8434-8294.4/9

=√139.69

=√15.5111

=3.9384

This is the right tailed test .

The null and alternative hypothesis is ,

H0 :    = 25

Ha : >25

Test statistic = t

= ( - ) / S / n

= (28.8 -25 ) / 3.94 / 10

= 3.050

Test statistic = t =  3.050

P-value =0.0069

= 0.01

P-value <

0.0069 < 0.01

Reject the null hypothesis .

There is sufficient evidence to suggest that