Question

Find a 95% confidence interval for the current true proportion

More Prahces We want to estimate the proportion of Philadelphia families with children enrolled in preschool. In a random sample of 50 Philadelphia families with children of preschool age, 35 had children enrolled in preschool. Find a 95% confidence interval for the current true proportion of Philadelphia families with the children enrolled in preschool.

Answer 1

Solution:

Confidence Interval for population proportion(p)

Given,

n = 50 ....... Sample size

x = 35 .......no. of successes in the sample

Let denotes the sample proportion.

     = x/n = 35/50 = 0.70

Our aim is to construct 95% confidence interval.

c = 0.95

= 1- c = 1- 0.95 = 0.05

  /2 = 0.05 2 = 0.025 and 1- /2 = 0.975

Search the probability 0.975 in the Z table and see corresponding z value

$Z_{alpha/2}$ = 1.96 for the 95% Confidence interval

Now , confidence interval for population proportion(p) is given by:

​

p-Marqin.of.error<P<D+ Margin.of error

     

0.70 -1.96*
уб.70(1-0.70),50
0.70 +1.96*
уб.70(1-0.70),50

0.70 - 0.12702251768 <     < 0.70 + 0.12702251768

0.5730 < <  0.8270

is the required 95% confidence interval for the population proportion.

Answer is (0.5730,0.8270)