4. Calculate the effect size for this hypothesis test. effect size = || %3D
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
Weight gain during pregnancy. In 2004, the state of North Carolina released to the public a large data set containing information on births recorded in this state. This data set has been of interest to medical researchers who are studying the relationship between habits and practices of expectant mothers and the birth of their children. The following histograms show the distributions of weight gain during pregnancy by 847 younger moms (less than 35 years old) and 132 mature moms (35 years old and over) who have been randomly sampled from this large data set. The average weight gain of younger moms is 30.64 pounds, with a standard deviation of 14.5 pounds, and the average weight gain of mature moms is 29.37 pounds, with a standard deviation of 13.56 pounds. Do these data provide strong evidence that there is a significant difference between the two population means? Conduct a hypothesis test.
Note: The degrees of freedom for this problem is df = 180.958463. Round all results to 4 decimal places. Remember not to round for intermediate calculations!
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