Question

2. We are interested in estimating the proportion of the population that exhibits characteristic y. In our random sample of n-196, we observe 25 instances of characteristic y. For a 95% confidence interval for P, what will be the upper interval limit?

Answer 1

Solution :

Given that,

n = 196

x = 25

Point estimate = sample proportion = = x / n = 25/196=0.128

1 -   = 1-0.128=0.872   

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

Z = Z0.05 = 1.645 ( Using z table )

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

= 1.645 (((0.128*0.872) /196 )

E = 0.039

A 95% upper confidence interval for population proportion p is ,

p < + E

p < 0.128 + 0.039

p <0.167