Question

A random sample of 1200 NAU students in Flagstaff found 384 NAU students who drink coffee daily. Find a 95% confidence interval for the true percent of NAU students in Flagstaff who drink coffee daily. Express your results to the nearest hundredth of a percent. .

Answer: _______ to _______ %

Please include work so I may better understand the problem.

Answer 1

Solution :

Given that,

n = 1200

x = 384

Point estimate = sample proportion = = x / n = 384 /1200=0.32

1 -   = 1- 0.32 =0.68

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z 0.025 = 1.96   ( Using z table )

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

= 1.96 (((0.32*0.68) /1200 )

E = 0.0264

A 95% confidence interval is ,

- E < p < + E

0.32-0.0264 < p < 0.32+0.0264

0.2936< p < 0.3464

Answer: ___29.36%___ to ___34.64____ %