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Sagot :
Answer and Step-by-step explanation:
To calculate a confidence interval for a proportion:
1) Determine the proportion
[tex]p=\frac{308}{500}[/tex]
p = 0.616
2) A 90% confidence interval has z-score that is 1.645.
3) Calculate margin of error
[tex]ME=\sqrt{\frac{p(1-p)}{n} }[/tex]
where
n is the sample size
So
[tex]ME=\sqrt{\frac{0.616(1-0.616)}{500} }[/tex]
[tex]ME=\sqrt{\frac{0.616(0.384)}{500} }[/tex]
ME = 0.02175
Then the interval is given by
p ± z(ME)
0.62 ± 1.645(0.02175)
0.62 ± 0.035
The interval will be
0.585 < p < 0.655
What this means is that we are 90% confident that the true proportion of Katy Perry's Twitter female followers is between 0.585 and 0.655.
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