Stat for Business and Econ Section 4 sign Out Saint Makwan Customer Support apli
ID: 3316817 • Letter: S
Question
Stat for Business and Econ Section 4 sign Out Saint Makwan Customer Support aplia Inference about a Population Graded Aslanment I .ad Chapter 12 1 Back to Assignment Due Thursday 12.07.17 at 0200 PM Attampts: Kaap the Highest: 0/2 16. Exercise 12.133 (Aloritbmic) state and out ct state tultion s supposed to re ce e nn bar oe students in state supportad unt ersities. The re tra or a un var ty ants to stimate propor on r, ot students who are payinq ut-ot state tultion on randam enn le e 70 turle is In live at star is taken and 50 n rhen, pav tutian an th-installment pan Find-aa fi int co d nce inter alfa r he d on the data. Rennd ynur a ra der mal pl Raisl a a nstalmant plan to late be compared with in state instal ert plan narers 99%, CI . Copyr ght NoticeExplanation / Answer
16.
TRADITIONAL METHOD
given that,
possibile chances (x)=50
sample size(n)=70
success rate ( p )= x/n = 0.714
I.
sample proportion = 0.714
standard error = Sqrt ( (0.714*0.286) /70) )
= 0.054
II.
margin of error = Z a/2 * (stanadard error)
where,
Za/2 = Z-table value
level of significance, = 0.01
from standard normal table, two tailed z /2 =2.576
margin of error = 2.576 * 0.054
= 0.139
III.
CI = [ p ± margin of error ]
confidence interval = [0.714 ± 0.139]
= [ 0.575 , 0.853]
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DIRECT METHOD
given that,
possibile chances (x)=50
sample size(n)=70
success rate ( p )= x/n = 0.714
CI = confidence interval
confidence interval = [ 0.714 ± 2.576 * Sqrt ( (0.714*0.286) /70) ) ]
= [0.714 - 2.576 * Sqrt ( (0.714*0.286) /70) , 0.714 + 2.576 * Sqrt ( (0.714*0.286) /70) ]
= [0.575 , 0.853]
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interpretations:
1. We are 99% sure that the interval [ 0.575 , 0.853] contains the true population proportion
2. If a large number of samples are collected, and a confidence interval is created
for each sample, 99% of these intervals will contains the true population proportion
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