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 of the null hypothesis of equal means?
g. Would the hypothesis that the means were the same versus a two-sided alternative be rejected at the significance level α = .1?
h. Suppose you know that the variance of the normal distribution was σ2 = 1. How would your answers to the preceding questions change?
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