1) In a survey of \(5,000\) Naperville residents, \(63\%\) of respondents named Cookie Dough Creations as their favorite ice cream place. What is the margin of error for this survey? What are the percentages that the “true” percentage is most likely between?
2) \(46\%\) of randomly sampled people said that Christmas is their favorite holiday. The margin of error for this survey was found to be \(2\%\). How many people were surveyed?
3) \(3966\) people were surveyed on the Time Capsule of Ice and Fire blog about whether they watched Game of Thrones before or after reading the books. \(62.2\%\) reported that they began watching the show first. (Source )
a) Construct a \(90\%\) confidence interval for the proportion of individuals who watched the show before beginning to read the books.
b) Construct a \(95\%\) confidence interval.
c) Construct a \(98\%\) confidence interval.
d) Interpret your results for part \(c\).
4) In a sample of people, a \(95\%\) confidence interval was constructed of \(0.56<p<0.62\), where \(p\) is the true proportion.
a) Find \(\hat{p}\), \(\sigma\) and \(n\).
b) How confident can we be that \(p>0.50\)?
Solution Bank
2) \(46\%\) of randomly sampled people said that Christmas is their favorite holiday. The margin of error for this survey was found to be \(2\%\). How many people were surveyed?
3) \(3966\) people were surveyed on the Time Capsule of Ice and Fire blog about whether they watched Game of Thrones before or after reading the books. \(62.2\%\) reported that they began watching the show first. (Source )
a) Construct a \(90\%\) confidence interval for the proportion of individuals who watched the show before beginning to read the books.
b) Construct a \(95\%\) confidence interval.
c) Construct a \(98\%\) confidence interval.
d) Interpret your results for part \(c\).
4) In a sample of people, a \(95\%\) confidence interval was constructed of \(0.56<p<0.62\), where \(p\) is the true proportion.
a) Find \(\hat{p}\), \(\sigma\) and \(n\).
b) How confident can we be that \(p>0.50\)?
Solution Bank