Posted: December 8th, 2016

# What role does variability within the sample play in determining statistical significance when testing hypotheses about µ?

What role does variability within the sample play in determining statistical significance when testing hypotheses about µ? In a certain jurisdiction, through 2010 the average sentence for defendants convicted of possession of marijuana was 24.5 months. In 2010 reforms that were designed to reduce the average sentence lengths for such offenses were undertaken. To investigate the effect of these reforms, a researcher selected a random sample of 24 cases from 2011. The mean length of a sentence in the sample was 21.2 months. Compute thep-value for a one-sided test if (i)S = 11.90 months, (ii)S = 7.95 months, and (iii)S = 4.62 months. You may assume that the conditions for the validity of the t-test are met. Write a sentence explaining the relationship between the value for S and the p-value. Does the relationship seem reasonable? [Use the Vassar applet to compute the p-value.]

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