Question

Random samples of 100 parts from production line A had 12 parts that were defective and 100 parts from production line B had 5 that were defective. What is the test statistic for the hypothesis test of a difference between the two proportions?

a. z = 2.16
b. z = 0.7
c. z = 1.77
d. z = 2.16

Answer 1

Option C) z = 1.77

Explanation:

We are given the following information in the question:

For line A:

`\text{Sample size}, n_1 = 100\\`

Number of defective part, x = 12

`p_1 = \displaystyle(x)/(n_1) = (12)/(100) = 0.12`

For line B:

`\text{Sample size}, n_2 = 100\\`

Number of defective part, y = 5

`p_2 = \displaystyle(y)/(n_2) = (5)/(100) = 0.05`

Test statistic =

`\displaystyle\frac{p_1-p_2}{\sqrt{p(1-p)((1)/(n_1)+(1)/(n_2))}}\\\\\text{where }p = (x+y)/(n_1+n_2) = (12+5)/(100+100) = (17)/(200) = 0.085`

Putting the values, we get:

`\text{Test statistic } = \displaystyle\frac{0.12-0.05}{\sqrt{0.085(1-0.085)((1)/(100)+(1)/(100))}} = 1.77`

Option C) z = 1.77