Question

d. (9.00 X U.U) (JU.U *1.73. The widths of copper lines in prin le widths of copper lines in printed circuit boards must be close to a design value. Three manufacturers were asked to prepare circuit boards with copper lines 0.500 um (micrometers) wide (1 um = 1 X 10 manufacturer's quality control department reported Ollowing line widths on five sample circuit boards (given in micrometers): Manufacturer 1 Manufacturer 2 Manufacturer 3 0.512 0.514 0.500 0.508 0.513 0.501 0.516 0.514 0.502 0.504 0.514 0.502 0.513 0.512 0.501 a. What is the mean and standard deviation of the data provided by each manufacturer? b. For which of the three sets of data does the 95% confidence interval include 0.500 um? c. Which of the data sets fit the description “precise and accurate," and which is “precise but not accurate"? 1 74 Diabete... ni

Answer 1

The mean can be calculated by adding all of the values and then dividing by the number of measurements (5). The values are:

Manufacturer 1: 0.511

Manufacturer 2: 0.513

Manufacturer 3: 0.501

The standard deviations represent how far are the measured values from the average value. They are:

Manufacturer 1: 0.005

Manufacturer 2: 0.001

Manufacturer 3: 0.001

The 95% confidence intervals are:

Manufacturer 1: from 0.507 to 0.515

Manufacturer 2: 0.512 to 0.514

Manufacturer 3: 0.500 to 0.502 (This is the one that includes the desired value)

Manufacturer 3 is both precise and accurate, while Manufacturer 2 is precise (low deviation) but not accurate (not close to the "real" value).

Answer 2

a. The mean of manufacturer 1 is

= $\frac{1}{5 }$ (0.512 + 0.508 + 0.516 + 0.504 + 0.513)

= 0.5106

The standard deviation of manufacturer 1 is

UA

= $\sqrt{\frac{0.0000872}{5}}$

= 0.00417

The mean of manufacturer 2 is

= $\frac{1}{5 }$ (0.514 +0.513+0.514+0.514+0.512)

= 0.5134

The standard deviation of manufacturer is

= $\sqrt{\frac{0.0000032}{5}}$

= 0.0008

The mean of manufacturer 3 is

= $\frac{1}{5 }$ (0.500 + 0.501+0.502+0.502+0.501)

The standard deviation of manufacturer 3 is

= $\sqrt{\frac{0.0000028}{5}}$

= 0.00075