Question

q2.A random sample of 121 observations produced a sample proportion of 0.35. An approximate 95% confidence interval for the population proportion p is between

a) 0.265 and 0.421 b) 0.307 and 0.393 c) 0.265 and 0.435 d) 0.245 and 0.455 e) 0.279 and 0.421

Answer 1

Solution :

Given that,

n = 121

Point estimate = sample proportion = =0.35

1 -   = 1-0.35 =0.65

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96   ( Using z table )

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

= 1.96 (((0.35*0.65) / 121)

E = 0.085

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.35-0.085 < p < 0.35+0.085

0.265 and 0.435