n northern climates, roads must be cleared of snow quickly tollowlig Sorm. s, ro
ID: 3045955 • Letter: N
Question
n northern climates, roads must be cleared of snow quickly tollowlig Sorm. s, roads e of storm severity is x -its duration in hours, while the effectiveness of sho can be quantified by x2 the number of hours crews, men, and machine, spend to clear snow. Here are the results for 25 incidents in Wisconsin. Table 3.2 Snow Data x2 2 12.5 13.7 9.0 24.43.5 26.1 14.5 16.5 6.5 18.2 8.0 14.5 8.0 17.4 10.5 22.017.5 42.3 9.0 11.0 10.0 32.5 10.5 17.5 19.5 23.6 4.5 18.7 12.0 21.8 8.0 13.2 7.0 15.8 6.0 10.4 9.0 32.1 8.5 15.6 13.0 25.6 7.0 12.3 6.5 12.0 7.0 11.8 8.0 12.8 (a) Find the sample mean and variance of the difference x2 x by first obtaining the summary statistics. (b) Obtain the mean and variance by first obtaining the individual values x for j 1,2,..., 25 and then calculating the mean and variance. Compare these values with those obtained in part a.Explanation / Answer
Answer:
a).
Descriptive statistics
x1
x2
count
25
25
mean
9.420
19.272
sample standard deviation
3.760
7.889
sample variance
14.139
62.239
minimum
3.5
10.4
maximum
19.5
42.3
range
16
31.9
Mean of (x2-x1) = mean of x2- mean x1 = 19.272-9.420 = 9.852
Variance of x2-x1 =var(x2)+var(x1) = 62.239+14.139 =76.378
b).
Descriptive statistics
x2-x1
count
25
mean
9.852
sample standard deviation
7.031
sample variance
49.433
minimum
1.2
maximum
24.8
range
23.6
Comparing the two methods, the means are same but the variances are not same. This may be due to the variables are not independent.
Descriptive statistics
x1
x2
count
25
25
mean
9.420
19.272
sample standard deviation
3.760
7.889
sample variance
14.139
62.239
minimum
3.5
10.4
maximum
19.5
42.3
range
16
31.9
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