ion 1 What do Americans do to conserve energy? The Assocated Press NORccenter to
ID: 3177161 • Letter: I
Question
ion 1 What do Americans do to conserve energy? The Assocated Press NORccenter tor public Affars Research conducted a survey of 1000 adults who had personaly done something to try ave eneruyinme uit year, and found the folowing percentages Turn down heat 26% Install more energy saving appliances 23% morebicycle more: 18% Unplug tings: 16% Americans who instal more energy saving appliances to conserve energy. Construct the 90% confidence interval estimate for the proportion Answers should be accurate up to 4 decimal places. tion 2 particular area. A random sample of 40 respondents is selectod, and each respondent A market researcher for a consumer electronics company wants to study the media viewing behavior of TV, oontent week is 41 hours with a standard deviation of 35 instructed to keep a record of time spent engaged content across al (traditional sample mean viewing time per game console, Intemet on a computer video on a video on a mobile phone) in a partouar week T interval estimate for the mean content viewing sme per week in this area. What is the margn of emor? construct a 99ms confidence Answers should be accurate up to 4 decimal places. Lower limtExplanation / Answer
Confidence Interval For Proportion
CI = p ± Z a/2 Sqrt(p*(1-p)/n)))
x = Mean
n = Sample Size
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
No. of success(x)=230
Sample Size(n)=1000
Sample proportion = x/n =0.23
Confidence Interval = [ 0.23 ±Z a/2 ( Sqrt ( 0.23*0.77) /1000)]
= [ 0.23 - 1.645* Sqrt(0) , 0.23 + 1.65* Sqrt(0) ]
= [ 0.208,0.252]
Interpretations:
1) We are 90% sure that the interval [0.208 , 0.252 ] contains the true population proportion
2) If a large number of samples are collected, and a confidence interval is created
for each sample, 90% of these intervals will contains the true population proportion
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