PSTAT 120B
PSTAT 120B
(c) For each of the values of n and p in the table below, calculate F(2) exactly and fill in the first empty column. Calculate the absolute difference between the exact probability and the approximation you calculated earlier and fill in the second empty column. Round to three decimal places.
PSTAT 120B
(d) Often it is said that the approximation is good when n is “large enough”. What do you notice about the approximation error as n increases?
PSTAT 120B
(e) However, “large enough” varies in different contexts. What do you notice about the approximation error for larger sample sizes when p is small? Do you think that n = 50 is sufficient to achieve a good approximation if p = 0.01?
Data on 134 Americans from the CDC’s National Health and Nutrition Examination Survey indicated that average BMI was 28.8 kg/m2. We will assume that the variance is 64. Let Yidenote the BMI of the ith survey respondent, and assume that the data are collected from a random sample of Americans. Let Y¯ denote the (random) sample mean and ¯y denote the (observed) sample mean 28.8.
(a) Identify any given parameters and quantities other than ¯y and write a transformation of Y¯ that is approximately standard normal. (The transformation can include unknown parameters, but any known parameters should be replaced by their given values.)
(b) Suppose that the mean BMI were the midpoint of the healthy range. Under this assumption, calculate the probability that the sample mean exceeds 28.8.
(c) Do you think the data suggest Americans are overweight on average? Why or why not?
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