Statistics and Probability Answers

If you are to conduct a test of hypothesis, what are your considerations on the type of statistic to be used? Why?

1. In a hypothesis test, the null hypothesis is rejected in favor of the alternative hypothesis. Does this mean that the alternative hypothesis is correct?

2. Between the two methods, which one do you prefer? Why?

When is it appropriate to use the t-distribution in testing a hypothesis about a population mean?

In what ways are the distributions of the z-statistic and the t-statistic alike?

Between the null and alternative hypothesis, it is the null hypothesis that is subject to a rigorous test. Can you change the model and subject the alternative hypothesis to a rigorous test? Explain your thinking.

What makes the normal curve a suitable model for decision-making?

2.  Show that

  (a) var(X – Y) = var(X) + var(Y) – 2cov(X,Y)                                                                                  (b) cov(X,aY + b) = acov(X,Y) if a and are constants.         

1.  Consider the following joint probability density function (pdf) of the random variables X and Y:   f(x,y)  =  0 ≤ x ≤ 6,    0 ≤ y ≤ 8     =  0  elsewhere                                                                           

Calculate the constant c if P(2 < X < c, 3 < Y < 5) = 0,06