Question 1161572: U.S. News & World Report carried an article concerning drug-related murders in the nation's capital. A sample of 112 days in 1987 revealed an average of three homicides per day in a increased to 4.2. If the respective standard deviations were 1.9 and 2.2 murders, does the interval suggest a difference in the incidence of homicides in 1988? Set a=0.05. Assume the population variances are equal.
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! This is a 2 sample t-test and assumed randomness. The pop variances are equal.
one can do t with df=222 (112-1)*2 or z because of the larger sample size.
Both test statistics are -4.37 which is highly significant with a p-value=0.0000193.
Given that calculating pooled degrees of freedom is a lot of work by hand, it is easier to do this on a calculator for the "correct" t-test. In the real world, with df=217.4, z would be fine, especially when the test statistic is very large.
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