Question

A man who moves to a new city sees that there are two routes he could take to work. A neighbor who has lived there a long time tells him Route A will average 5 minutes faster than Route B. The man decides to experiment. Each day he flips a coin to determine which way to go, driving each route 10 days. He finds that Route A takes an average of 48

?minutes, with standard deviation 44 minutes?,
and Route B takes an average of 49 minutes, with standard deviation 1 minute.
Histograms of travel times for the routes are roughly symmetric and show no outliers. Complete parts a and b. Use alpha?equals=0.05

Answer 1

0.3 to 2.3 min

Explanation:

n1=n2=10

x1=48

x2=49

s1=4

s2=1

Determine the deegres of freedom.

`\delta=(((s_1^2)/(n_1)+(s_2^2)/(n_2))^2)/((((s_1^2)/(n1))^2)/(n_1-1)+(((s_1^2)/(n1))^2)/(n_2-1))=10.14`

t=2.037 (student's appendix)

`E=t\sgrt((s_1^2)/(n_1)+(s^2_2)/(n_2))=1.3`

`(x_1-x_2)-E=(48-49)-1.3=-2.3`

`(x_1-x_2)+E=(48-49)+1.3=0.3`

We are 95% confident that average commuting time for rute A is between 0.3 and 2.3 min shorter than for rute B.