Problem sheet 3 -- Hypothesis testing, correlation coefficients, and covariance

Hypothesis testing

A professor wants to know if her introductory statistics class has a good grasp of basic math. Six students are chosen at random from the class and given a math proficiency test. The professor wants the class to be able to score above 70 on the test. The six students get scores of 62, 92, 75, 68, 83, and 95. Can the professor have 90 percent confidence that the mean score for the class on the test would be above 70?

Covariance and correlation coefficients I

  • Show that the covariance is linear in its arguments.

    Covariance and correlation coefficients II

  • Consider a normally distributed random variable X with mean zero and variance sigma_X^2=5 and a normally distributed random variable Y with mean zero and variance sigma_Y^2=10. We want to consider the variables U=X+2Y and V=4X-3Y.