Given the following i.i.d. observations of a random variable Y: 16.0, 12.0, 14.0

Question

Given the following i.i.d. observations of a random variable Y: 16.0, 12.0, 14.0, 13.4, 16.0, 12.5 (a) Calculate the sample mean, sample variance, and sample standard deviation. (b) Calculate an alpha = 0.05 confidence interval for the mean, using the Central Limit Theorem approximation. (c) Calculate an alpha = 0.05 confidence interval for the mean, using Student's t-distribution. (A table is posted on the eLearning website.) (d) Estimate how many measurements you would need to make in order to get a confidence interval for the mean that is plusminus 1.0 wide. Answer this using both the Central Limit Theorem and the t-distribution.

Explanation / Answer

(A)

(B)

(C)

(D)

Sample Mean 13.9833 Sample Variance 2.9217 Sample Std. dev. 1.7093

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