A manufacturing company produces bearings. One line of bearings is specified to

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.

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