Question

A student wants to determine if the proportion of grey emus to brown emus is a constant throughout the population. She found the in 30 emu farms she surveyed, the proportion of grey emus to brown emus is 0.46. She wants to develop a 90% confidence interval.What is the lower limit of a 90% confidence interval for this proportion?

Answer 1

Solution :

Given that,

n = 30

Point estimate = sample proportion = = x / n = 0.46

1 - = 1 - 0.46 =0.54

At 90% confidence level

= 1 - 90%  

= 1 - 0.90 =0.10

=0.10

Z = Z_{0.10 =} 1.28

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

= 1.28 (((0.46*0.54) / 30)

= 0.1165

A 90% confidence interval for population proportion p is ,

- E

0.46 - 0.1165

0.3435

The 90% confidence interval for the population proportion p is :lower limit 0.3435