Question

A random sample of 100 childrens fiction books was taken at my local library. Of these 100 books, 47 were written by women. Using the information provided, calculate a 92% confidence interval for the population proportion.

please provide upper/lower bound intervals and step by step solution.

Answer 1

Solution :

Given that,

n = 100

x = 47

= x / n = 47 / 100 = 0.47

1 - = 1 - 0.47 = 0.53

At 92% confidence level the z is ,

= 1 - 92% = 1 - 0.92 = 0.08

/ 2 = 0.08 / 2 = 0.04

Z_/2 = Z_0.04 = 1.751

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

= 1.751 * (((0.47*0.53) /100 )

= 0.087

A 92% confidence interval for population proportion p is ,

- E < P < + E

0.47 - 0.087 < p < 0.47 + 0.087

0.383< p < 0.557

The 92% confidence interval for the population proportion p is : (0.383 , 0.557)

lower bound = 0.383

upper bound = 0.557