Question

Mrs. Edward's kindergarten class was counting a random sample of blocks. They counted 107 blue blocks and 144 green blocks. Calculate the 90 percent confidence interval for the population proportion of the blue blocks?

Answer 1

Solution :

Given that,

n = 144

x = 107

= x / n = 107 / 144 =0.743

1 - = 1 - 0.743 = 0.257

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

Z_/2 = Z_0.05 = 1.645

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

= 1.645 * (((0.743 * 0.257) / 144)

= 0.060

A 90 % confidence interval for population proportion p is ,

- E < P < + E

0.743 - 0.060 < p < 0.743 + 0.060

0.683 < p < 0 803

The 90% confidence interval for the population proportion p is : ( 0.683 , 0.803)