Question

Construct a 95% confidence interval of the population proportion using the given information.

x = 45, n = 150

The lower bound is

The upper bound is

(Round to three decimal places as needed.)

Answer 1

Answer:

95% confidence interval of the population proportion is  (0.227, 0.373)

Step-by-step explanation:

Confidence Interval can be calculated using p±ME where

• p is the population proportion ($\frac{45}{150} =0.3$

• ME is the margin of error from the mean

and margin of error (ME) around the mean can be found using the formula

ME=$\frac{z*\sqrt{p*(1-p)}}{\sqrt{N} }$ where

• z is the corresponding statistic in 95% confidence level (1.96)

• p is the population proportion (0.3)

• N is the sample size (150)

then ME=$\frac{1.96*\sqrt{0.3*0.7}}{\sqrt{150} }$ ≈ 0.073

Then 95% confidence interval would be 0.3±0.073 or (0.227, 0.373)