Question

A random sample of 500 residents from Shinbone, Kansas, shows that exactly 50 of the respondents had been victims of violent crime over the past year. Estimate the proportion of victims for the population as a whole, using the 90% confidence interval. (HINT: Calculate the sample proportion Ps before using Formula 7.3. Remember that proportions are equal to frequency divided by N.)

Answer 1

Solution:

Confidence Interval for population proportion(p)

Given,

n = 500 ....... Sample size

x = 50 .......no. of successes in the sample

Let denotes the sample proportion.

     = x/n   = 50/500 = 0.10

Our aim is to construct 90% confidence interval.

c = 0.90

= 1- c = 1- 0.90 = 0.10

  /2 = 0.10 2 = 0.05 and 1- /2 = 0.950

Search the probability 0.950 in the Z table and see corresponding z value

= 1.645 for the 90% Confidence interval

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

     

0.10 -1.645* 0.10 +1.645*

0.078 <     <   0.122

is the required 90% confidence interval for the population proportion.

(0.078 ,0.122)