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emmainna [20.7K]
2 years ago
9

g "They hired an analyst who collected a random sample of 40,361 Game of Thrones fans, and found that 8,337 of those fans said t

hat they like Season 8. Using this data, the analyst wants to estimate the actual proportion of fans who like Season 8. What is the lower bound for a 90% confidence interval? Give your answer to 4 decimal places."
Mathematics
1 answer:
Viktor [21]2 years ago
6 0

Answer:

The lower bound for a 90% confidence interval is 0.2033.

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 = 40361, \pi = \frac{8337}{40361} = 0.2066

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}} = 0.2066 - 1.645\sqrt{\frac{0.2066*0.7934}{40361}} = 0.2033

The lower bound for a 90% confidence interval is 0.2033.

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