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Margaret [11]
2 years ago
13

In 2015 as part of the General Social Survey, 1289 randomly selected American adults responded to this question:

Mathematics
1 answer:
Radda [10]2 years ago
5 0

Answer:

B (0.312, 0.364)

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:

1289 randomly selected American adults responded to this question. This means that n = 1289.

Of the respondents, 436 replied that America is doing about the right amount. This means that \pi = \frac{436}{1289} = 0.3382.

Determine a 95% confidence interval for the proportion of all the registered voters who will vote for the Republican Party. ​

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}} = 0.3382 - 1.96\sqrt{\frac{0.3382*0.6618}{1289}} = 0.312

The upper limit of this interval is:

\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.3382 + 1.96\sqrt{\frac{0.3382*0.6618}{1289}} = 0.364

The 95% confidence interval is:

B (0.312, 0.364)

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