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.
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
= Z0.05 = 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
Get Answers For Free
Most questions answered within 1 hours.