Question

1.A researcher collects a sample of 30 individuals who have a mean age of 34.6, a median age of 41.5, and a modal age of 44. Make one observation regarding the nature of the distribution of data that the researcher collected.  What would be the best measure of central tendency to use in describing a distribution of this form?  Whydid you choose the measure of central tendency that you did?

2.A statistician computes a 95% confidence interval for the number of prior arrests of those convicted of violent crimes. The interval ranged from 1.6 to 3.6 prior arrests.  Given these data, what is the probability that the population mean is greater than 3.6 prior arrests?  Why?

Answer 1

1. Here Mean<Median<Mode

Thus the data seem to be negatively skewed.

Then an appropriate measure would be median because the measures like mean are affected by unusually higher or lower values. In a negatively skewed distribution, higher values occur with higher frequency and hence mean may be misleading . Similarly mode will be near the cluster of the higher values and will be misleading to represent the central tendency.

2. Since the 95% confidence interval ranged from (1.6,3.6) , the chance that it contains the true population mean is .95. Thus the true mean is outside this interval with chance .05. If we assume that the the confidence interval is equal tailed, the chance of falling beyond either boundary of the interval is equal and is .025. Thus the chance  that the population mean is greater than 3.6 (i.e. falling beyond the right boundary of the interval) prior arrests is .025.

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