Question

Out of 500 people sampled, 85 had kids. Based on this, construct a 95% confidence interval for the true population proportion of people with kids.

Give your answers as decimals, to three places

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Answer 1

The values provided in the above questions are as below

n = 500

x = The sampled people has kids = 85

We find the sample proportion is as below

We construct a 95% confidence interval for the true population proportion of people with kids using following formula

The value is find using Excel function

Here, confidence level = 95% = 0.95

1 - = 0.95

= 0.05 that is /2 = 0.025

We find the using following Excel function

=NORMSINV(probability)

Here, probability =  /2 = 0.025

=NORMSINV(0.025) then press Enter, we get

(Round answer up to 2 decimal places)

We find 95% confidence interval for the true population proportion of people with kids using above values

We write above answer up to 3 decimal places is as

Which is also written as below

The 95% confidence interval for the true population proportion of people with kids are (0.137, 0.203)

Summary :-

The 95% confidence interval for the true population proportion of people with kids are (0.137, 0.203)