Brenna owns 9 T-shirts, 3 of which are red.
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The confidence interval would be
.
We use the formula
, where
, with p being the sample proportion and N being the sample size.
First we find the z-score associated with this level of confidence:
Convert 95% to a decimal: 95/100 = 0.95
Subtract from 1: 1-0.95 = 0.05
Divide by 2: 0.05/2 = 0.025
Subtract from 1: 1-0.025 = 0.975
Using a z-table (http://www.z-table.com) we see that this value is associated with a z-score of 1.96.
Since 578/720 said yes, this gives us p=0.80:
This gives us
We use the formula
First we find the z-score associated with this level of confidence:
Convert 95% to a decimal: 95/100 = 0.95
Subtract from 1: 1-0.95 = 0.05
Divide by 2: 0.05/2 = 0.025
Subtract from 1: 1-0.025 = 0.975
Using a z-table (http://www.z-table.com) we see that this value is associated with a z-score of 1.96.
Since 578/720 said yes, this gives us p=0.80:
This gives us