A survey concluded that 87% (out of 3079) of males in a given state have health

Question

A survey concluded that 87% (out of 3079) of males in a given state have health insurance. a) Examine the conditions for constructing a confidence interval for the proportion of males in the given state who had health insurance. b) Find the 95% confidence interval for the percent of males who have health insurance. c) Interpret your confidence interval. a) Check the assumptions and conditions. Choose the correct answer below. A. This was a random sample of more than 10% of all males in a given state: the sample is too large. B. The independence assumption is violated; whether one male in a given state is "less likely" to have health insurance is dependent on whether another male in the same state is "less likely" to have health insurance. C. This was a random sample of less than 10% of all males in a given state; there are less than 10 successes, so the sample is not large enough. D. This was a random sample of less than 10% of all males in a given state: there were at least 10 successes and 10 failures, so the sample is large enough. The

Explanation / Answer

a) Option D is correct.

b) The statistical software output for 95% confidence interval is:

One sample proportion confidence interval:
p : Proportion of successes
Method: Standard-Wald

95% confidence interval results:

Hence,

95% confidence interval is:

(0.858, 0.882)

Interpretation:

We are 95% confident that the true proportion of males in a given state that have health insurance lies between 0.858 and 0.882

Proportion Count Total Sample Prop. Std. Err. L. Limit U. Limit p 2678.73 3079 0.87 0.0060607512 0.85812115 0.88187885

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