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In order to check the claim that the pregnancy length of women who smoke during pregnancy is shorter, on average, than the pregnancy length of women who do not smoke, a random sample of 35 pregnant women who smoke and a random sample of 35 pregnant women who do not smoke were chosen and their pregnancy lengths were recorded. Here is a figure of this example:
The null hypothesis in this case is which claims that pregnancy length related to (or affected by) whether or not the woman smokes during pregnancy.
The alternative hypothesis in this case is which claims that pregnancy length related to (or affected by) whether or not the woman smokes during pregnancy.
Note that "mu" stands for the Greek letter μ, the population mean—mu1 stands for the mean of population 1 and mu2 stands for the mean of population 2.