How do you calculate a 95% confidence interval without the mean?

In 2007, the Pew Research Center assessed public opinion of the challenges of motherhood. Over a 4-week period, they surveyed 2020 Americans. They found 60% of respondents felt that it was more difficult to be a mother today than it was 20 or 30 years ago.

How do you calculate the 95% confidence interval to estimate the percentage of Americans who believe that it is more difficult to be a mother today than it was 20 or 30 years ago?

1 Answer
Will
May 6, 2017

[.58,.62]

Explanation:

you can do confidence intervals using proportions. You can use normal distribution if the amount of items is greater than 10 for both outcomes. Variance is estimated as p(1-p)

CI = z * se where z is the z statistic you get from the z table at the 95% and se is the standard error . Since this is a two tail test it should be 1.96 thus
CI = z *sqrt((p(1-p))/n)

CI = 1.96 * sqrt((.6(.4))/2020)

~~ .6 +- .021 or [.58,.62]

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