1 The result of a roll of a fair die is a discrete probabili

1. The result of a roll of a fair die is a discrete probability distribution with possible values of 1, 2, 3, 4, 5 or 6 with equal probabilities. We determined that the expected value (?) of this distribution is 3.5 and the variance (?2) is 2.92. You plan to take a sample size n=101 from this distribution (i.e., you roll the die 101 times).

a) You perform the experiment and get a sample mean of 4.2. Use this sample mean to calculate a 95% confidence interval for the true mean. Note whether the confidence interval contains the value of the expected mean for a fair die.

b) Give an interpretation of your confidence interval. Also, does your confidence interval give you reason to suspect the die is not fair?

c) Your experiment resulted in a sample variance of 2.67. Is it appropriate to use this statistic to calculate a confidence interval for the population variance? If yes, calculate the confidence interval. If no, explain why not.

Solution

a) Sample mean =4.2

std error = sigma/rtn = 1.708/rt101 = 0.171

Margin of error =