Question

In a survey of 235 randomly selected CGCC students, 170 of them have taken an online class.

a. Construct, by hand, a 90% confidence interval for the proportion of all CGCC students that have taken an online class.

b. Interpret your confidence interval in context of the data.

Answer 1

Solution :

Given that,

n = 235

x = 170

Point estimate = sample proportion = = x / n = 170/235=0.723

1 - = 1 - 0.723=0.277

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 (((0.723*0.277) /235 )

E = 0.0480

A 90% confidence interval for population proportion p is ,

- E < p < + E

0.723 - 0.0480 < p < 0.723 +0.0480

0.6750< p < 0.7710

interpret =The 90% confidence interval for the population proportion p is : 0.6750, 0.7710