Question

Construct a confidence interval of the population proportion at the given level of confidence. x equals 175 comma n equals 250 comma 90 % confidence

The lower bound is _____.

The upper bound is _____. ​(Round to three decimal places as​ needed.)

Answer 1

Solution :

Given that,

n = 250

x = 175

Point estimate = sample proportion = = x / n = 175 / 250 = 0.700

1 - = 1 - 0.700 = 0.300

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.10 = 0.10

/ 2 = 0.10 / 2 = 0.05

Z_/2 = Z_0.05 = 1.645

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

= 1.645 * (((0.700 * 0.300) / 250)

= 0.048

A 90% confidence interval for population proportion p is ,

- E < p < + E

0.700 - 0.048 < p < 0.700 + 0.048

0.652 < p < 0.748

(0.652 , 0.748)

Lower bound = 0.652

Upper bound = 0.748

< p <