Homework: Exam #3 Practice Score: 0 of 1 pt Section 9.2 Exercise 14 A survey of

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Homework: Exam #3 Practice Score: 0 of 1 pt Section 9.2 Exercise 14 A survey of 150 students is selecled randomly on a large university campus They are asked it they use a laptop in class to take notes The resut of the survey is that 72 of the 150 students responded "yes." Save 20f 12 ( 1 complete) Score: 8.33%, 1 of 12 pts Question Help * An approximate 95% contence "terval is (0 396 0 562) which one tow ng are true? " they are not true, beny explain why r a) 96% of the shaerts tat r, the interval (0 396 0562) b) The bue proportion of students who use laplops to take nles is captured in the interval (0 398.0 562) with probability 095 c) There a 48% chance that a student uses a laptop to take notes d) There a 95% chance that t 48% of the time the student uses a laplop to take notes e) We are 95% co ent that the true proportion of students who use laptops to take notes is captured nne nterva eo 391 o

Explanation / Answer

9.2 section exercise 14

TRADITIONAL METHOD
given that,
possibile chances (x)=72
sample size(n)=150
success rate ( p )= x/n = 0.48
I.
sample proportion = 0.48
standard error = Sqrt ( (0.48*0.52) /150) )
= 0.041
II.
margin of error = Z a/2 * (stanadard error)
where,
Za/2 = Z-table value
level of significance, = 0.05
from standard normal table, two tailed z /2 =1.96
margin of error = 1.96 * 0.041
= 0.08
III.
CI = [ p ± margin of error ]
confidence interval = [0.48 ± 0.08]
= [ 0.4 , 0.56]
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DIRECT METHOD
given that,
possibile chances (x)=72
sample size(n)=150
success rate ( p )= x/n = 0.48
CI = confidence interval
confidence interval = [ 0.48 ± 1.96 * Sqrt ( (0.48*0.52) /150) ) ]
= [0.48 - 1.96 * Sqrt ( (0.48*0.52) /150) , 0.48 + 1.96 * Sqrt ( (0.48*0.52) /150) ]
= [0.4 , 0.56] = (0.398,0.562)
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interpretations:
1. We are 95% sure that the interval [ 0.4 , 0.56] contains the true population proportion
2. If a large number of samples are collected, and a confidence interval is created
for each sample, 95% of these intervals will contains the true population proportion

option:e
We are 95% sure that the interval [ 0.398 , 0.562] contains the true population proportion

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