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Mama L [17]
3 years ago
15

Suppose that twelve bats was used in the experiment. For each trail, the zoo keeper pointed to one of two "feeders". Suppose tha

t the bats went to the correct feeder (the one that the zoo keeper pointed at) 9 times. Find the 95% confidence interval for the population proportion of times that the bats would follow the point.
Mathematics
1 answer:
marshall27 [118]3 years ago
5 0

Answer:

The 95% confidence interval for the population proportion of times that the bats would follow the point is (0.505, 0.995).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \pi, and a confidence interval 1-\alpha, we have the following confidence interval of proportions.

\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}

In which

Z is the zscore that has a pvalue of 1 - \frac{\alpha}{2}

For this problem, we have that:

There are 12 bats, and 9 would follow the feeder. This means that n = 12 and \pi = \frac{9}{12} = 0.75.

Find the 95% confidence interval for the population proportion of times that the bats would follow the point.

So \alpha = 0.05, z is the value of Z that has a pvalue of 1 - \frac{0.05}{2} = 0.975, so z = 1.96.

The lower limit of this interval is:

\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.75 - 1.96\sqrt{\frac{0.75*0.25}{12}} = 0.505

The upper limit of this interval is:

\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.75 + 1.96\sqrt{\frac{0.75*0.25}{12}} = 0.995

The 95% confidence interval for the population proportion of times that the bats would follow the point is (0.505, 0.995).

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