1. A study is conducted to analyze internet privacy for teens. A group of \(50\) teens is randomly sampled and \(47\) report clicking on links from unknown email addresses. Construct a \(90 \%\) confidence interval for the true proportion of teens that click on links from unknown email addresses or explain what conditions prevent you from applying our methods.

  2. A study is conducted to analyze internet privacy for teens. A group of \(50\) teens is randomly sampled and \(17\) report clicking on links from unknown email addresses. Construct a \(90 \%\) confidence interval for the true proportion of teens that click on links from unknown email addresses or explain what conditions prevent you from applying our methods.

  3. Politcal experts claim that only \(35 \%\) of registered voters vote in local elections. A recent political poll (assume they are using methods that ensure independence) asks \(1000\) registered voters if they plan to vote in their next local election. The poll finds that \(840\) registered voters will vote in the next election.

3a. What is the standard error for the sampling distribution of the sample proportion?

3b. Construct a \(95 \%\) confidence interval for the true population proportion.

3c. Does your answer to the previous part support or challenge the claim of the political experts? Explain your reasoning by making reference to the confidence interval.

  1. The error bound for the proportion \(EBP\) is calculated by \(EBP = z_{\alpha/2}\cdot SE = z_{\alpha/2}\cdot \sqrt{p(1-p)/n}\). Will the \(EBP\) be bigger when \(p=0.2\) or \(p=0.4\)? You don’t need to know the sample size or confidence level to answer this.

  2. For what value of \(p\) is the \(EBP\) as big as possible?

  3. Suppose you want to estimate the proportion of registered voters that will vote in a local election. Before doing any polling you set the goal to make sure that that you estimate a range of values that has an \(EBP\) for less than \(3 %\) with \(95 \%\) confidence. That is, you want to say “We are \(95 \%\) confident that the true proporion of people that will vote in a local election is between $ -3 %$ and $ +3 %$”. Determine how big your sample size should be to guarantee this?

  4. A university newspaper is conducting a survey to determine what fraction of students support a $ $ 200$ per year increase in fees to pay for a new stadium. How big of a sample is required to ensure the \(EBP\) is smaller than \(5 \%\) with \(95 \%\) confidence?