Question

A large poll showed that 42%, percent of adults approved of their nation's prime minister. Margot wants to test if it is now lower, so she takes a random sample of 1,000 adults in that nation and finds that 390—or 39% percent of those sampled—approved of the prime minister.
Let p represent the proportion of adults in this nation who approve of the prime minister.

Which of the following is an appropriate set of hypotheses for her significance test?

Choose 1 answer:

(Choice A)
A
\begin{aligned} &H_0: p = 0.39 \\ &H_\text{a}: p < 0.39 \end{aligned}
​

H
0
​
:p=0.39
H
a
​
:p<0.39
​


(Choice B)
B
\begin{aligned} &H_0: p = 0.39 \\ &H_\text{a}: p < 0.42 \end{aligned}
​

H
0
​
:p=0.39
H
a
​
:p<0.42
​


(Choice C)
C
\begin{aligned} &H_0: p = 0.42 \\ &H_\text{a}: p < 0.39 \end{aligned}
​

H
0
​
:p=0.42
H
a
​
:p<0.39
​


(Choice D)
D
\begin{aligned} &H_0: p = 0.42 \\ &H_\text{a}: p < 0.42 \end{aligned}
​

H
0
​
:p=0.42
H
a
​
:p<0.42
​

Answer 1

According to the situation described, the appropriate set of hypotheses for her significance test is given by:

$H_0: p = 0.42$.

$H_1: p < 0.42$.

What are the hypothesis tested?

At the null hypothesis, it is tested if the proportion is still of 42%, that is:

$H_0: p = 0.42$.

At the alternative hypothesis, it is tested if the proportion is now lower, that is:

$H_1: p < 0.42$.

Hence, the the appropriate set of hypotheses for her significance test is given by:

$H_0: p = 0.42$.

$H_1: p < 0.42$.

More can be learned about an hypothesis test at brainly.com/question/26454209