Question 1 is already completed in the table. I need help with question 2, which

Question

Question 1 is already completed in the table. I need help with question 2, which utilizes figure from the table (explained in question 1). Thanks! . sum m5 v5 m10 v10 m50 v50 dage Variable Obs Mean Std. Dev. Min Max 4.79141 500 130.5108 92.88259 33.796 3.598283 21.4 4.3 24.4 47 538.5 500 33.692 m5 V5 m10 v10 m50 500 500 133.9856 62.97953 14.32222 411.3778 500 33.51444 1.296592 30.44 37.7 v50 dage 500 129.9597 21.12727 66.78204 183.4139 144 33.63194 11.46277 69 1. Based on the program 'samples.do' (described below), randomly (with replacement) generate 500 sample means (xbar) and variances (varx) for the variable dage using samples of sizes n=5, 10, 50. 2. Demonstrate that: a. the expectation of the sample means is equal to the population mean (assume the original mean for donor age, N=144, is the population); of dage divided by the sample size; and dage. b. the variance of the sample means is approximately equal to the original variance c. the expectation of the sample variance is equal to the population variance of

Explanation / Answer

2a) To demonstrate that the expectation of the sample means is equal to the population mean (of dage):

The population mean is 33.63194

The expectation of sample means = mean of sample means weighted by sample proprtions

= (mean_m5*5/65) + (mean_m10*10/65) + (mean_m50*50/65) = 2.592 + 5.199 + 25.78 = 33.571 which is very close to the population mean.

2b) The variance of the sample means

=variance(33.692,33.796,33.51444,each taken 500 times) = 0.013513

And the variance of dage = 11.462772 = 131.395 and when divided by sample size of 144*65, the equal to 0.014.

hence the variance of sample means and the actual variance divided by the sample size are almost equal.

2c) The expectation of sample variance = [ (130.5108*5/65) + (133.9856*10/65) + (129.9597*50/65) ] = 130.621

and the population variance of dage = 131.395.

Hence the expectation of sample variance is almost equal to the population variance.

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