Respuesta :
Answer: B) [-0.0332,0.1332]
Step-by-step explanation: Confidence Interval is an interval where we can be a percentage sure the true mean is.
The confidence interval for a difference in population proportion is calculated following these steps:
First, let's find population proportion for each population:
[tex]p_{1}=\frac{30}{120}=0.25[/tex]
[tex]p_{2}=\frac{32}{160}=0.2[/tex]
Second, calculate standard deviation for each proportion:
[tex]\sigma_{1}=\sqrt{\frac{0.25(0.75)}{120} } = 0.0395[/tex]
[tex]\sigma_{2}=\sqrt{\frac{0.2(0.8)}{160} } = 0.0316[/tex]
Now, we calculate standard error for difference:
[tex]SE=\sqrt{\sigma_{1}^{2}+\sigma_{2}^{2}}[/tex]
[tex]SE=\sqrt{0.0395^{2}+0.0316^{2}}[/tex]
SE = 0.0505
The z-score for a 90% CI is 1.645.
Then, confidence interval is
[tex]p_{1}-p_{2}[/tex] ± z-score.SE
[tex]0.25-0.2[/tex] ± [tex]1.645(0.0505)[/tex]
0.05 ± 0.0831
The limits of this interval are:
inferior: 0.05 - 0.0831 = [tex]-0.0332[/tex]
superior: 0.05 + 0.0831 = 0.1332
The 90% confidence interval for the difference in the population proportion of pit pulls and golden retrievers is [tex][-0.0332,0.1332][/tex].
