You have been employed as a marketing executive by the Coca-Cola company to evaluate their progress in the century-long "cola war" with Pepsi. To gather some up to date data on preferences, you have carried out a survey of a simple random sample of 125 high school children and asked them whether they prefer Coke or Pepsi. Of these, 47 replied that they prefer Coke and the remainder said they prefer Pepsi.

1. Carry out a hypothesis test for whether Coke is less preferred than Pepsi among high school children. Use the 5% level of significance and acriticalvalue decision rule.
2. Compute a 95% confidence interval for the proportion of high school children who prefer Coke.
3. Is there a relationship between this confidence interval and the finding of the hypothesis test in question 1? Explain.