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Westkost [7]
3 years ago
13

A random sample of 225 items from a population results in 60% possessing a given characteristic. Using this information, the res

earcher constructs a 99% confidence interval to estimate the population proportion. The resulting confidence interval is _______.
Mathematics
1 answer:
Dmitrij [34]3 years ago
8 0

Answer: (0.52,\ 0.68)

Step-by-step explanation:

The formula for a \alpha- level confidence interval for the population proportion:-

p\pm z_{\alpha/2}\times\sqrt{\dfrac{p(1-p)}{n}}

Given : n = 225 ; p = 0.60 ; \alpha= 1-0.99=0.01

By using the given information , the confidence interval for the population proportion:-

0.6\pm z_{0.005}\times\sqrt{\dfrac{0.6(1-0.6)}{225}}\\\\=0.6\pm(2.576)(0.0327)\\\\=0.6\pm0.08\\\\=0.6-0.08,\ 0.6+0.08\\\\=(0.52,\ 0.68)

Hence, the resulting confidence interval is (0.52,\ 0.68) .

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