Systolic blood pressures from two simple random samples of the same population h

Question

Systolic blood pressures from two simple random samples of the same population have the same sums of squared deviations from their means. Sample 1 has 200 observations and sample 2 has 400 observations. Both samples are symmetrical. Which ones of the following is/are true? Correct false statements.

1) The average of the deviations from the mean in both samples is zero.

2) The standard deviation of sample 2 is larger than the standard deviation of sample 1.

3) Roughly speaking, the average distance of the observations from the mean in sample 1 is smaller than the same measure for sample 2.

4) The distribution of sample 1 has a larger spread around the sample mean than does the distribution of sample 2

5) The standard deviation from sample 1 is a parameter

6) The varience of sample 1 is a statistic that is sensitive to extreme values (outliers)

Explanation / Answer

Answers:

1

True, because we know that the sum of deviations from the mean is always zero for symmetrical data.

2

False, because sample size for sample 2 is larger than sample 1 which indicate that SD for sample 2 is smaller than sample 1 given the condition of same sums of squared deviations.

3

False, because average distance of the observations from the mean is depends on spread of distribution.

4

True, because sample size for sample 1 is small and both samples have same sums of squared deviations from the means.

5

False, because standard deviation from sample 1 is a statistic and not a parameter.

Note, parameter is associated with population, while statistic is associated with sample.

6

True, because variance is associated with sample observations although it contains outliers. Statistic is defined as the function of sample observations.

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