Question

Question 19 8 pts A city planner is researching why traffic speeds appear to be slower throughout the city. She checks 51 speed measurement devices located around the city and computes a sample mean of 20.6 mph. The historical mean speed for the city is approximately normal with u = 21.9 mph and o = 8.9 mph. What is the 95% confidence interval for the true mean speed? BIVA HTML Editor A: I = = = = = x x = = V DTH 12pt O words

Answer 1

n=51

=20.6

T

$\sigma$=8.9

#95% Confidence interval for the true mean speed is

(
T
-Z$\alpha$/2*$\sigma$/sqrt(n)<$\mu$<
T
+Z$\alpha$/2*$\sigma$/sqrt(n))

At 95%  Z$\alpha$/2 ie Z0.05/2=Z0.025=1.96

(20.6-1.96*8.9/sqrt(51)<$\mu$<20.6+1.96*8.9/sqrt(51))

(20.6-2.44<$\mu$<20.6+2.44)

(18.16<$\mu$<23.04)

95% Confidence interval for the true mean speed is between 18.16 and 23.04