Answer:
The 90% confidence interval for pis (0.7342, 0.8658).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of
, and a confidence level of
, we have the following confidence interval of proportions.
![\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}](https://tex.z-dn.net/?f=%5Cpi%20%5Cpm%20z%5Csqrt%7B%5Cfrac%7B%5Cpi%281-%5Cpi%29%7D%7Bn%7D%7D)
In which
z is the zscore that has a pvalue of
.
For this problem, we have that:
100 rats mothers, 80 went right. So ![n = 100, \pi = \frac{80}{100} = 0.8](https://tex.z-dn.net/?f=n%20%3D%20100%2C%20%5Cpi%20%3D%20%5Cfrac%7B80%7D%7B100%7D%20%3D%200.8)
90% confidence level
So
, z is the value of Z that has a pvalue of
, so
.
The lower limit of this interval is:
![\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.8 - 1.645\sqrt{\frac{0.8*0.2}{100}} = 0.7342](https://tex.z-dn.net/?f=%5Cpi%20-%20z%5Csqrt%7B%5Cfrac%7B%5Cpi%281-%5Cpi%29%7D%7Bn%7D%7D%20%3D%200.8%20-%201.645%5Csqrt%7B%5Cfrac%7B0.8%2A0.2%7D%7B100%7D%7D%20%3D%200.7342)
The upper limit of this interval is:
![\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.8 + 1.645\sqrt{\frac{0.8*0.2}{100}} = 0.8658](https://tex.z-dn.net/?f=%5Cpi%20%2B%20z%5Csqrt%7B%5Cfrac%7B%5Cpi%281-%5Cpi%29%7D%7Bn%7D%7D%20%3D%200.8%20%2B%201.645%5Csqrt%7B%5Cfrac%7B0.8%2A0.2%7D%7B100%7D%7D%20%3D%200.8658)
The 90% confidence interval for pis (0.7342, 0.8658).