Respuesta :
Answer:
(B) 0.2843
Step-by-step explanation:
Let d be the difference in proportions from Country X and Country Y who were first married between the ages of 18 and 32.
Then hypotheses are
[tex]H_{0}[/tex]: d=0.15
[tex]H_{a}[/tex]: d<0.15
Test statistic can be found using the equation
[tex]z=\frac{p1-p2-0.15}{\sqrt{{p*(1-p)*(\frac{1}{n1} +\frac{1}{n2}) }}}[/tex] where
- p1 is the sample proportion of Country X (0.36)
- p2 is the sample proportion of Country Y (0.26)
- p is the pool proportion of p1 and p2 ([tex]\frac{60*0.36+50*0.26}{50+60}=0.31[/tex])
- n1 is the sample size of adults from Country X (60)
- n2 is the sample size of adults from Country Y (50)
Then [tex]z=\frac{0.36-0.26-0.15}{\sqrt{{0.31*0.69*(\frac{1}{60} +\frac{1}{50}) }}}[/tex] ≈ 0.5646
p-value of test statistic is ≈ 0.2843
p-value states the probability that the difference in proportions between a random sample of 60 adults from Country X and a random sample of 50 adults from Country Y who were first married between the ages of 18 and 32 is at least 0.15
The closest to the probability can be identified by estimating the standard deviation with help of standard deviation we can find p-value.
The correct option is (B).
Given:
Sample proportion of Country X is [tex]P_1=\dfrac{36\%}{100}=0.36[/tex].
Sample proportion of Country Y is [tex]P_2=\dfrac{26\%}{100}=0.26[/tex].
The sample size of adults from Country X [tex]n_1=60[/tex].
The sample size of adults from Country Y [tex]n_2=50[/tex].
Let the difference in proportions is [tex]x[/tex].
Consider the hypotheses.
[tex]H_0:\:d=0.15[/tex]
[tex]H_a:d<0.15[/tex]
Calculate the pool proportion.
[tex]p=\dfrac {p_1\times n_1+p_2\times n_2}{n_1+n_2}[/tex]
Substitute the value.
[tex]p=\dfrac {60\times 0.36+50\times 0.26}{50+60}\\p=0.31[/tex]
Calculate the test statistic.
[tex]z=\dfrac{p_1-p_2-0.15}{\sqrt{p(1-p)\times \left (\dfrac{1}{n_1}+\dfrac{1}{n_2}\right)}}[/tex]
Substitute the value.
[tex]z=\dfrac{0.36-0.26-0.15}{\sqrt{0.31(1-0.31)\times \left (\dfrac{1}{60}+\dfrac{1}{60}\right)}}\\z=0.5646[/tex]
Thus, the p-value would be [tex]0.2843[/tex].
Therefore, The correct option is (B).
Learn more about what p-value is here:
https://brainly.com/question/16534415
