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In: Statistics and Probability

A Pew Poll conducted in 2017 surveyed a random sample of 200 adult Americans and 75...

A Pew Poll conducted in 2017 surveyed a random sample of 200 adult Americans and 75 of them said that they had seen a ghost. Find a 99% confidence interval for the percentage of all Americans who believe they have seen a ghost. Interpret your interval. Round to three decimal places.

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Expert Solution

Solution :

Given that,

n = 200

x = 75

Point estimate = sample proportion = = x / n = 75/200=0.375

1 -   = 1- 0.375 =0.625

At 99% confidence level the z is ,

  = 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z/2 = Z0.005 = 2.576 ( Using z table )

  Margin of error = E =   Z / 2     * (((( * (1 - )) / n)

= 2.576* (((0.375*0.625) /200 )

E = 0.088

A 99% confidence interval for population proportion p is ,

- E < p < + E

0.375-0.088< p <0.375+ 0.088

0.287< p < 0.463

The 99% confidence interval for the population proportion p is0.287, 0.463

orchestra answered 1 year ago
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