Are they both used to calculate the confidence interval at 95% for a population proportion?Here are two questions from my book.In a survey in a large city, 170 households out of 250 owned a pet. Find the 95% confidence interval for the proportion of households in the city who own a pet.From a random sample, 136 out of 400 people experience discomfort after receiving a vaccine. Construct a 95% confidence interval for the population proportion who might experience discomfort.For each question do I use: p^±1n or p^±p(1−p)n?

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rywleob8 · Accepted Answer

Step 1Multiple errors here: Apparently you want a 95% CI for binomial success probability p, using the number of successes X observed in n independent trials, giving p^ as an estimate of p.Provided n is large enough for the normal approximation to apply, and for p^ to be a reasonably good estimate of p, an approximate 95% confidence interval for p isp^±1.96p^(1−p^)n.In case, p^≈12, the factor 1.96p^(1−p^)n is very nearly 1n.My guess is that you are expected to use the displayed expression to work your problems.Step 2Considerable theoretical, computational, and simulation evidence has shown that an interval that works much better for sample sizes such as those in your problem is as follows: Use p~=X+2n+4 to estimate p and use n~ instead of n in the formula above to obtain the &#039;Agresti-Coull&#039; (or &#039;Plus Four&#039;) confidence interval:p~±1.96p~(1−p~)n~.

Are they both used to calculate the confidence

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