What role does variability within the sample play in determining statistical significance when

testing hypotheses about ? In a certain jurisdiction, through 2017 the average sentence for

defendants convicted of possession of marijuana was 24.5 months. In 2017 reforms were

undertaken that were designed to reduce the average sentence lengths for such offences. To

investigate the effect of these reforms, a researcher selected a random sample of 24 such cases

from 2018. The mean length of sentence in the sample was 21.2 months. Compute the p-value

for a one-sided test if (i) S = 11.90 months, (ii) S = 7.95 months, (iii) S = 4.62 months. You may

assume that the conditions for the validity of the t test are met. explain

the relationship between the value for S and the p-value. Does the relationship seem reasonable?

[Use R to compute the p-value.]