Answered question

2022-03-24

Answer & Explanation

RizerMix

RizerMix

Expert2023-04-25Added 656 answers

First, we need to calculate the sample proportion, which is denoted by p-hat. We can find p-hat by dividing the number of successes by the sample size. Thus,

p^=xn=64160=0.4

Next, we need to calculate the critical value z* for a 95% confidence interval. We can find this value using a standard normal distribution table or a calculator. For a 95% confidence interval, the z* value is 1.96.

Then, we can construct the confidence interval using the formula:

p^±z(p-1-p^^n)

Substituting the values we have calculated, we get:

0.4±1.96(0.41-0.4160)

Simplifying this expression, we get:

0.4±0.079

Therefore, the 95% confidence interval estimate for the population proportion p is:

0.321p0.479

This means that we are 95% confident that the true population proportion falls within this interval.

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