Question

8. If a simple random sample of 215 students was surveyed, and it was found that 90 of them have iPhones, what is the 90% confidence interval estimate of the proportion of all students who have iPhones?

Answer 1

Solution :

Given that,

n = 215

x = 90

Point estimate = sample proportion = = x / n = 90/215=0.419

1 -   = 1- 0.419 =0.581

At 90% confidence level the z is

= 1 - 90% = 1 - 0.90 = 0.1

/ 2 = 0.1 / 2 = 0.05

Z/2 = Z0.05 = 1.645 ( Using z table )

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

= 1.645 *((0.419*0.581) / 215)

= 0.0554

A 90% confidence interval for population proportion p is ,

- E < p < + E

0.419- 0.0554< p <0.419+ 0.0554

0.3636< p < 0.4744

The 90% confidence interval for the population proportion p is : 0.3636 ,0.4744