Statistics: Informed Decisions Using Data (4th Edition)

Published by Pearson
ISBN 10: 0321757270
ISBN 13: 978-0-32175-727-2

Chapter 11 - Section 11.3 - Assess Your Understanding - Applying the Concepts - Page 563: 13b

Answer

$t_0\gt t_α$: null hypothesis is rejected. There is enough evidence to conclude that the ramp meters are effective in maintaining a higher speed on the freeway.

Work Step by Step

$x ̅_1,n_1~and~s_1$ refer to ramp meters on and $x ̅_2,n_2~and~s_2$ refer to ramp meters off. $x ̅_1=\frac{∑x_{1_i}}{n_1}=40.667$ $s_1=\sqrt {\frac{∑(x_{1_i}-x ̅_1)^2}{n_1}}=10.040$ $x ̅_2=\frac{∑x_{2_i}}{n_2}=34.533$ $s_2=\sqrt {\frac{∑(x_{2_i}-x ̅_2)^2}{n_2}}=9.561$ $H_0:~µ_1=µ_2$ versus $H_1:~µ_1\gt µ_2$ $t_0=\frac{(x ̅_1-x ̅_2)-(µ_1-µ_2)}{\sqrt {\frac{s^2_1}{n_1}+\frac{s^2_2}{n_2}}}=\frac{(40.667-34.533)-0}{\sqrt {\frac{10.040^2}{15}+\frac{9.561^2}{15}}}=1.714$ $n=15$, so: $d.f.=n-1=14$ Left-tailed test: $t_α=t_{0.10}=1.345$ (According to Table VI, for d.f. = 14 and area in right tail = 0.10) Since $t_0\gt t_α$, we reject the null hypothesis.
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