Question

Construct a 99​% confidence interval to estimate the population proportion with a sample proportion equal to 0.90 and a sample size equal to 250.

------A 99% confidence interval estimates that the population proportion is between a lower limit of ___ and an upper limit of ___.

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Answer 1

Solution :

Given that,

n = 250

Point estimate = sample proportion = = 0.90

1 -   = 1-0.90 =0.10

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* (((0.90*0.10) / 250)

= 0.049

A 99% confidence interval for population proportion p is ,

- E < p < + E

0.90-0.049 < p < 0.90+0.049

0.851< p < 0.949

A 99% confidence interval estimates that the population proportion is between a lower limit of _0.851__ and an upper limit of _0.949__.