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

Answer:

Option C) z = 1.77

Step-by-step 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

$p_1 = \displaystyle\frac{x}{n_1} = \frac{12}{100} = 0.12$

For line B:

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

Number of defective part, y = 5

$p_2 = \displaystyle\frac{y}{n_2} = \frac{5}{100} = 0.05$

Test statistic =

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

Putting the values, we get:

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

Option C) z = 1.77