Question

a simple random sample of 324 College student showed that 105 of them agree with a certain law construct a 90% confidence interval estimate of the proportion of students who agree with this law

Answer 1

Solution :

Given that,

n = 324

x =105

Point estimate = sample proportion = = x / n = 105/324=0.324

1 - = 1-0.324=0.676

At 90% confidence level

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z_{0.05 = 1.645} ( Using z table )

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

= 1.645 (((0.324*0.676) / 324)

E= 0.0428

A 90% confidence interval for population proportion p is ,

- E < p < + E

0.324 -0.0428 < p <0.324 + 0.0428

0.281< p < 0.367

(0.281, 0.367)

The 90% confidence interval for the population proportion p is : (0.281, 0.367)