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Orlov [11]
3 years ago
6

The poll found that 38% of a random sample of 1012 American adults said they believe in ghosts. What is the lower bound for a 90

% confidence interval for the percentage of all American adults who believe in ghosts?
Mathematics
1 answer:
Brrunno [24]3 years ago
6 0

Answer:

The lower bound for a 90% confidence interval for the percentage of all American adults who believe in ghosts is 0.3549

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 level of 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:

n = 1012, \pi = 0.38

90% confidence level

So \alpha = 0.1, z is the value of Z that has a pvalue of 1 - \frac{0.1}{2} = 0.95, so Z = 1.645.

The lower limit of this interval is:

\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.38 - 1.645\sqrt{\frac{0.38*0.62}{1012}} = 0.3549

The lower bound for a 90% confidence interval for the percentage of all American adults who believe in ghosts is 0.3549

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