Rodrigo works for a company that ships orders from two different locations—location A and location B. He wonders if the same proportion of orders arrive late from each location. He takes a random sample of orders from each location to test if there is a significant difference in the proportion of orders that arrive late from each location.
Which of the following is an appropriate set of hypotheses for Rodrigo's significance test?
Choose 1 answer:
Choose 1 answer:

(Choice A)
A
\begin{aligned} &H_0: p_\text{A} - p_\text{B}=0\\ &H_\text{a}: p_\text{A} - p_\text{B} <0 \end{aligned}
​

H
0
​
:p
A
​
−p
B
​
=0
H
a
​
:p
A
​
−p
B
​
<0
​


(Choice B)
B
\begin{aligned} &H_0: p_\text{B} - p_\text{A}=0\\ &H_\text{a}: p_\text{B} - p_\text{A} <0 \end{aligned}
​

H
0
​
:p
B
​
−p
A
​
=0
H
a
​
:p
B
​
−p
A
​
<0
​


(Choice C)
C
\begin{aligned} &H_0: p_\text{A} - p_\text{B}=0\\ &H_\text{a}: p_\text{A} - p_\text{B} \neq 0 \end{aligned}
​

H
0
​
:p
A
​
−p
B
​
=0
H
a
​
:p
A
​
−p
B
​


​
=0
​


(Choice D)
D
\begin{aligned} &H_0: p_\text{B} - p_\text{A}\neq0\\ &H_\text{a}: p_\text{B} - p_\text{A} =0 \end{aligned}
​

H
0
​
:p
B
​
−p
A
​


​
=0
H
a
​
:p
B
​
−p
A
​
=0
​