Answer: B) [-0.0332,0.1332]
Step-by-step explanation: <u>Confidence</u> <u>Interval</u> 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:
![p_{1}=\frac{30}{120}=0.25](https://tex.z-dn.net/?f=p_%7B1%7D%3D%5Cfrac%7B30%7D%7B120%7D%3D0.25)
![p_{2}=\frac{32}{160}=0.2](https://tex.z-dn.net/?f=p_%7B2%7D%3D%5Cfrac%7B32%7D%7B160%7D%3D0.2)
Second, calculate standard deviation for each proportion:
![\sigma_{1}=\sqrt{\frac{0.25(0.75)}{120} } = 0.0395](https://tex.z-dn.net/?f=%5Csigma_%7B1%7D%3D%5Csqrt%7B%5Cfrac%7B0.25%280.75%29%7D%7B120%7D%20%7D%20%3D%200.0395)
![\sigma_{2}=\sqrt{\frac{0.2(0.8)}{160} } = 0.0316](https://tex.z-dn.net/?f=%5Csigma_%7B2%7D%3D%5Csqrt%7B%5Cfrac%7B0.2%280.8%29%7D%7B160%7D%20%7D%20%3D%200.0316)
Now, we calculate standard error for difference:
![SE=\sqrt{\sigma_{1}^{2}+\sigma_{2}^{2}}](https://tex.z-dn.net/?f=SE%3D%5Csqrt%7B%5Csigma_%7B1%7D%5E%7B2%7D%2B%5Csigma_%7B2%7D%5E%7B2%7D%7D)
![SE=\sqrt{0.0395^{2}+0.0316^{2}}](https://tex.z-dn.net/?f=SE%3D%5Csqrt%7B0.0395%5E%7B2%7D%2B0.0316%5E%7B2%7D%7D)
SE = 0.0505
The z-score for a 90% CI is 1.645.
Then, confidence interval is
± z-score.SE
± ![1.645(0.0505)](https://tex.z-dn.net/?f=1.645%280.0505%29)
0.05 ± 0.0831
The limits of this interval are:
inferior: 0.05 - 0.0831 = ![-0.0332](https://tex.z-dn.net/?f=-0.0332)
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
.