solution

A computer was used to generate four random numbers from a normal distribution with a set mean and variance: 1.1650, .6268, .0751, .3516. Five more random normal numbers with the same variance but perhaps a different mean were then generated (the mean may or may not actually be different): .3035, 2.6961, 1.0591, 2.7971, 1.2641.

a What do you think the means of the random normal number generators were? What do you think the difference of the means was?

b What do you think the variance of the random number generator was?

c What is the estimated standard error of your estimate of the difference of the means?

d Form a 90% confidence interval for the difference of the means of the random number generators.

e In this situation is it more appropriate to use a one-sided test or a two-sided test of the equality of the means?

f What is the p-value of a two-sided test that the means were the same?

g Would the hypothesis that the means were the same versus a two-sided alternative be rejected at the significance level a = .1?

h Suppose you know that the variance of the normal distribution was o-2= 1. How would your answers to the preceding questions change?

 
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