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Westkost [7]
2 years ago
9

Use the sample data and confidence level to construct the confidence interval estimate of the population proportion p. n equals

550 comma x equals 440 comma 95 % confidence nothingless thanpless than nothing ​(Round to three decimal places as​needed.)
Mathematics
1 answer:
Alekssandra [29.7K]2 years ago
3 0

Answer:

(0.767,0.833)

Step-by-step explanation:

The 95% confidence interval for population proportion p can be computed as

p-z_{\frac{\alpha }{2} } \sqrt{\frac{pq}{n} }

The z-value associated with 95% confidence level is 1.96.

whereas p=x/n

We are given that x=440 and n=550.

p=440/550=0.8

0.8-1.96\sqrt{\frac{0.8(0.2)}{550} }

0.8-1.96\sqrt{\frac{0.16}{550} }

0.8-1.96\sqrt{0.00029 }

0.8-1.96(0.01706)

0.8-0.03343

0.76657

Thus, the required confidence interval is

0.767<P<0.833  (rounded to 3 decimal places)

Hence, we are 95% confident that our true population proportion will lie in the interval (0.767,0.833)

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Step-by-step explanation:

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<em></em>

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