Class Exercise 10

Problem 1

Say, you want to know the average $R$-score of the population of students at Vanier College. The Registrar's office would not give you the data, so you sample at random $82$ Vanier college students and find that the average $R$-score in this sample is $28.1$ with sample standard deviation of $5.1$.
  1. Construct a $95\%$ confidence interval for the $R$-score of the population of students at Vanier College.
  2. Write a sentence explaining why the shape of the true distribution of $R$-scores is not important in this calculation.

Problem 2

A sample of $44$ urban coywolves had an average weight of $18.2\, kg$ with standard deviation of $3.0\,kg$. A sample of $67$ non-urban coywolves had an average weight of $16.5\,kg$ with standard deviation of $2.8\,kg$.
  1. Construct $98\%$ confidence intervals for the population mean weights of the urban coywolves and of the non-urban coywolves.
  2. Can you claim with $98\%$ confidence that the urban coywolves are heavier than the non-urban ones? Explain.