Have American males (AMs) gotten heavier over the last 20 years? A random sample 77 AMs in 2019 had a mean weight of x = 189.030 pounds. A random sample 93 AMs in 1999 had a mean weight of y = 184.795 pounds. It is recognized that the true standard deviation of 2019 AMs weights is σx = 14.04 pounds while it is recognized that the true standard deviation of 1999 AMs weights is σy = 10.03 pounds. The true (unknown) mean of 2019 AMs weights is μx pounds, while the true (unknown) mean of 1999 AMs weights is μy pounds. Weights are known to be a normally distributed. In summary: Type Sample Size Sample Mean Standard Deviation 2019 Data (X) 77 189.030 14.04 1999 Data (Y) 93 184.795 10.03 a)Calculate the variance of the random variable X which is the mean of the weights of the 77 AMs from 2019. b)Calculate the variance of the random variable Y, which is the mean of the weights of the 93 AMs from 1999. c) Calculate the variance of X - Y?
Have American males (AMs) gotten heavier over the last 20 years? A random sample 77 AMs in 2019 had a
= 14.04 pounds while it is recognized that the true standard deviation of 1999 AMs weights is
= 10.03 pounds. The true (unknown) mean of 2019 AMs weights is
pounds, while the true (unknown) mean of 1999 AMs weights is
pounds. Weights are known to be a
| Type | Sample Mean | Standard Deviation | |
|---|---|---|---|
| 2019 Data (X) | 77 | 189.030 | 14.04 |
| 1999 Data (Y) | 93 | 184.795 | 10.03 |
a)Calculate the variance of the random variable X which is the mean of the weights of the 77 AMs from 2019.
b)Calculate the variance of the random variable Y, which is the mean of the weights of the 93 AMs from 1999.
c) Calculate the variance of X - Y?
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