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In: Statistics and Probability

Determine confidence intervals for each of the following. Percent = 67%; sample size = 300, confidence...

Determine confidence intervals for each of the following.

Percent = 67%; sample size = 300, confidence level = 95%

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Expert Solution

Solution :

Given that,

n = 300

Point estimate = sample proportion = = 67%=0.67

1 -   = 1-0.67 =0.33

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96   ( Using z table )

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

= 1.96 (((0.67*0.33) /300 )

E = 0.092

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.67-0.092 < p < 0.67+0.092

(0.578,0.762)

orchestra answered 2 years ago
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