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VLD [36.1K]
3 years ago
6

A study involves 669 randomly selected deaths, with 31 of them caused by accidents. construct a 98% confidence interval for the

true percentage of all deaths that are caused by accidents.
Mathematics
1 answer:
Alekssandra [29.7K]3 years ago
4 0

Answer:

Confidence Interval : 2.72% < p < 6.48%

Step-by-step explanation:

Number of randomly selected deaths = 669

Number of deaths caused by accident = 31

\text{Sample Proportion, p = }\frac{31}{669}=0.046

z-score for 98% confidence level = 2.326

\text{Margin of Error = }z\times \sqrt{\frac{p\cdot (1-p)}{n}}\\\\\text{Margin of error = }2.326\times \sqrt{\frac{0.046\times 0.954}{669}}\\\\\implies\text{Margin of error = }0.0188

Confidence Interval : 0.046 - 0.0188 < p < 0.046 + 0.0188

                                 : 0.0272 < p < 0.0648

                                 : 2.72% < p < 6.48%

Hence, Confidence Interval : 2.72% < p < 6.48%

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