A manufacturing company produces bearings. One line of bearings is specified to
ID: 3352735 • Letter: A
Question
A manufacturing company produces bearings. One line of bearings is specified to be 1.7 centimeters (cm)
in diameter. A major customer requires that the variance of the bearings be no more than .002 cm 2 . The
producer is required to test the bearings before they are shipped, and so the diameters of 16 bearings are
measured with a precise instrument, resulting in the following values. Assume bearing diameters are
normally distributed. Use the data and = .01 to test the data to determine whether the population of
these bearings is to be rejected because of too high a variance.
1.7
0
1.6
2
1.6
3
1.7
0
1.6
6
1.6
3
1.6
5
1.7
5
1.6
4
1.6
9
1.5
7
1.7
2
1.6
0
1.6
6
1.6
5
1.65
Explanation / Answer
Here,
H0 : 2 0.002 cm2
Ha : 2 > 0.002 cm2
Variance of sample s2 = 0.0021
sample size n = 16
Test statistic
X2 = (n-1)s2/02
X2 = (16 - 1) * 0.0021/ 0.0020 = 15.75
at alpha = 0.01 level
X2critical = X20.01,15 = 30.578
so here X2 < X2critical
we fail to reject the null hypothesis and can conclude that the varaince is not too much high and bearings cannot be rejected.