points MintroSat9 &E.075; My Notes A recent report summarized the results of a s
ID: 3336119 • Letter: P
Question
points MintroSat9 &E.075; My Notes A recent report summarized the results of a survey on how people get their news. Of the 2352 people in the survey who own a desktop or laptop, 1657 reported that they get their news from the desktop or laptop. (a) Identiry the sample size and the count. sample size (b) Find the sample proportion and ts standard error. (Round your answers to four decimal places (c) Find and interpret the 95% confidence interval for the population proportion. (Round your answers to thrt decimal places.) 95% 4f the time, the sample proportion will be between, lover value of end en upper velue of (d) Are the guidelines for use of the large-sample confidence intervel satisfied? Explain your answer. The guidelines[-Solect-s) satisfied, since the number of successes and failures in the sample are both! …Soloct-. TutorialExplanation / Answer
5.
TRADITIONAL METHOD
given that,
possibile chances (x)=1657
sample size(n)=2352
success rate ( p )= x/n = 0.705
I.
sample proportion = 0.705
standard error = Sqrt ( (0.705*0.295) /2352) )
= 0.009
II.B9
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 * 0.009
= 0.018
III.
CI = [ p ± margin of error ]
confidence interval = [0.705 ± 0.018]
= [ 0.686 , 0.723]
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DIRECT METHOD
given that,
possibile chances (x)=1657
sample size(n)=2352
success rate ( p )= x/n = 0.705
CI = confidence interval
confidence interval = [ 0.705 ± 1.96 * Sqrt ( (0.705*0.295) /2352) ) ]
= [0.705 - 1.96 * Sqrt ( (0.705*0.295) /2352) , 0.705 + 1.96 * Sqrt ( (0.705*0.295) /2352) ]
= [0.686 , 0.723]
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interpretations:
1. We are 95% sure that the interval [ 0.686 , 0.723] 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
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