Highway engineers in Alberta are painting white stripes on a highway. The stripe
ID: 3178140 • Letter: H
Question
Highway engineers in Alberta are painting white stripes on a highway. The stripes are supposed to be approximately 3 m long. However, because of the machine, the operator, and the motion of the vehicle carrying the equipment, considerable variation occurs among the stripe lengths. Engineers claim that the variance of stripes is not more than 0.41 m^2. Use the sample lengths given here from 12 measured stripes to test the variance claim. Assume stripe length is normally distributed. Let sigma = 0.05. Round your answer to 2 decimal places. The value of the test statistic is X^2 =Explanation / Answer
x
3.14
2.8
2.83
2.87
3.17
2.99
2.99
3.26
3.2
3.08
3.02
3.17
First we need to find sample variance (s^2)
s^2 = S ( x – x bar)^2 / (n-1)
x bar = Sx / n = 36.52 / 12 = 3.0433
x
( x - x bar)
( x - x bar)^2
3.14
0.0967
0.0094
2.8
-0.2433
0.0592
2.83
-0.2133
0.0455
2.87
-0.1733
0.0300
3.17
0.1267
0.0161
2.99
-0.0533
0.0028
2.99
-0.0533
0.0028
3.26
0.2167
0.0470
3.2
0.1567
0.0246
3.08
0.0367
0.0013
3.02
-0.0233
0.0005
3.17
0.1267
0.0161
Total =
0.2553
s^2 = S ( x – x bar)^2 / (n-1)
=0.2553 / 11
= 0.0232
Test Statistics:
X^2 = (n-1)*(s/sigma)^2 = (12-1)*(0.0232/0.41) = 0.62
X^2 = 0.62
The critical value for 11 degress of freedom at 5% level of significance is given by 19.675. The test statistics is less than the critical value so we fail to reject the null hypothesis.
Answer:
X^2 = 0.62
We fail to reject the null hypothesis.
Here the variance claim is true.
x
3.14
2.8
2.83
2.87
3.17
2.99
2.99
3.26
3.2
3.08
3.02
3.17
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