1) Example: The World Health Organization (WHO) monitors many variables to assess population overall health. One of these variables is birth weight. A low birth weight is defined as 2500 grams or less. Suppose that babies in a town had a mean birth weight of 3,500 grams with a standard deviation of 500 grams in 2005. This year, a random sample of 25 babies has a mean weight of 3,400 grams. Obviously, this sample weighs less on average than the population of babies in the town in 2005. A decrease in the town's mean birth weight could indicate a decline in the overall health of the town. Are differences this large in mean expected in random sampling from a population with a birth weight of 3,500 grams? What is the probability that 25 babies will have a random sample mean birth weight of 3,400 grams or less? We assume that the variability, as it was in 2005, in individual birth weights is the same this year. In general, the distribution of birth weights in a large population can be modeled by a normal curve. Identify the following: μ, σ, x, and n from the information given above:
b) Verify that a normal curve can be used to model the distribution of means for this situation. Label the mean and standard deviation (SD) in the normal model for the population and the sampling distribution, and for individual birth weights (grams).
Sample mean birth weight: Random samples of 10 babies