Question

A crayon manufacturer is comparing the effects of two kinds of yellow dye on the brittleness of crayons. Dye B is more expensive than dye A, but it is thought that it might produce a stronger crayon. Eight crayons were tested, four with each kind of dye, and the impact strength (in joules) was measured for each. The results are as follow:

Dye A: 1.0 2.0 1.2 3.0

Dye B: 3.0 3.2 2.6 3.4

a. If you wish to detect a true difference in impact strength of 1.4 joules for the two dyes, what would the appropriate sample size be if the mean and standard deviation for dye A is 1.8 and 0.91 respectively, and the mean and standard deviation for dye B is 3.05 and 0.34 respectively? You want the power of the test to be 90% and alpha = 0.05

b. Was this sample large enough?

Answer 1

First find pooled standard deviation of two sample:

n1 =4, s1 = 0.91, n2 = 4 and s2 = 0.34

Using Minitab:

Steps:

Stat-->Power and Sample Size--> 2 Sample t

Click on Option for Alpha:

Then Click to Ok and Ok:

Output:

(b): No, the sample size 4 for both groups not large enough.

sample size should be 7 for both groups where difference 1.4, power 0.90(or 90%) and alpha 0.05(or 5%).

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