Question 6.EX.5: Samples of 3-volt batteries from two manufacturers yielded t...
Samples of 3-volt batteries from two manufacturers yielded the following outputs, measured in volts:
| Brand A | 3.1 | 3.2 | 2.9 | 3.3 | 2.8 | 3.1 | 3.2 |
| Brand B | 3.0 | 3.0 | 3.2 | 3.4 | 2.7 | 2.8 |
Test whether there is any difference in the variance of output voltage of batteries from the two companies. Why might the variance be an important consideration for the manufacturer or for customers?
The two variances are s^{2}_{A}=0.031 and s^{2}_{B}=0.066. We therefore form the ratio F = 0.066/0.031 = 2.09, which has an F distribution with 6 and 7 degrees of freedom.
The 5% critical value is therefore 3.87 and the null is not rejected. There appears to be no differences between manufacturers. The variance is important because consumers want a reliable product – they would not be happy if their MP3 player worked with one battery but not another.