A manufacturer of television tubes has two types of tubes, A and B, respectively, the tubes have mean lifetimes of
xA = 1495 hours and xB = 1875 hours, and standard deviation of SA = 280 hours and SB = 310 hours. Which tube has the greater (a) absolute dispersion and (b) relative dispersion?
The weights of 10 boxes of a children brand of cereal have a mean content of 278 grams with an S.D of 9.64 grams. If these boxes were purchased at 10 different stores and the average price per box is $ 1.29 with an S.D of $ 0.09, can you conclude that the weights are relatively more homogeneous than the prices?
To determine which tube has the greater absolute dispersion, we can compare the standard deviations of the two types of tubes. The formula for absolute dispersion is the standard deviation multiplied by a constant factor.
(a) Absolute Dispersion:
The formula for absolute dispersion is given by:
Absolute Dispersion = Standard Deviation * Constant Factor
The constant factor is chosen based on the desired level of confidence. For a 95% confidence level, the constant factor is approximately 1.96.
So, for Tube A:
Absolute Dispersion A = Standard Deviation A * 1.96
= 280 * 1.96
For Tube B:
Absolute Dispersion B = Standard Deviation B * 1.96
= 310 * 1.96
Now, we can compare the absolute dispersions of Tube A and Tube B. The tube with a higher absolute dispersion value will have a greater dispersion of values.
(b) Relative Dispersion:
To calculate relative dispersion, we need to calculate the coefficient of variation (CV) for each tube. The coefficient of variation is the ratio of the standard deviation to the mean, expressed as a percentage.
The formula for CV is given by:
CV = (Standard Deviation / Mean) * 100
For Tube A:
CV A = (Standard Deviation A / Mean A) * 100
= (280 / 1495) * 100
For Tube B:
CV B = (Standard Deviation B / Mean B) * 100
= (310 / 1875) * 100
Now, we can compare the coefficient of variation for Tube A and Tube B. The tube with a higher coefficient of variation will have a greater relative dispersion.